Critical Infrastructures Risk and Vulnerability Assessment in Transportation of Dangerous Goods Transportation by Road and Rail ( PDFDrive.com )

Topics in Safety, Risk, Reliability and Quality
Bogdan I. Vamanu
Adrian V. Gheorghe
Polinpapilinho F. Katina
Critical Infrastructures:
Risk and Vulnerability
Assessment in
Transportation of
Dangerous Goods
Transportation by Road and Rail
Topics in Safety, Risk, Reliability and Quality
Volume 31
Series editor
Adrian V. Gheorghe, Old Dominion University, Norfolk, VA, USA
Editorial Advisory Board
Hirokazu Tatano, Kyoto University, Kyoto, Japan
Enrico Zio, Ecole Centrale Paris, France and Politecnico di Milano, Milan, Italy
Andres Sousa-Poza, Old Dominion University, Norfolk, VA, USA
More information about this series at http://www.springer.com/series/6653
Bogdan I. Vamanu Adrian V. Gheorghe
Polinpapilinho F. Katina
•
Critical Infrastructures:
Risk and Vulnerability
Assessment in Transportation
of Dangerous Goods
Transportation by Road and Rail
123
Bogdan I. Vamanu
Department of Life and Environmental
Physics, DFVM
Horia Hulubei National Institute for Physics
and Nuclear Engineering
Bucharest
Romania
and
European Commission’s Joint Research
Centre
Institute for Energy and Transport
(JRC-IET)
Ispra
Italy
Adrian V. Gheorghe
Engineering Management and Systems
Engineering
Old Dominion University
Norfolk, VA
USA
Polinpapilinho F. Katina
Engineering Management and Systems
Engineering
Old Dominion University
Norfolk, VA
USA
ISSN 1566-0443
ISSN 2215-0285 (electronic)
Topics in Safety, Risk, Reliability and Quality
ISBN 978-3-319-30929-3
ISBN 978-3-319-30931-6 (eBook)
DOI 10.1007/978-3-319-30931-6
Library of Congress Control Number: 2016935215
© Springer International Publishing Switzerland 2016
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
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The use of general descriptive names, registered names, trademarks, service marks, etc. in this
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The publisher, the authors and the editors are safe to assume that the advice and information in this
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Printed on acid-free paper
This Springer imprint is published by Springer Nature
The registered company is Springer International Publishing AG Switzerland
To my parents
—Bogdan I. Vamanu
To my children, Anastasia, Alexandra,
and Paul
—Adrian V. Gheorghe
To my mother, Elizabeth, sister, Rachel,
and niece, Beatrice
—Polinpapilinho F. Katina
Preface
The twentieth and twenty-first centuries have been characterized as tumultuous
(Martin 2006; Tainter 1988). This characterization fits within the scope of concepts
of ambiguity, complexity, emergence, independency, and uncertainty (Keating et al.
2014; Katina 2015). Ambiguity is associated with an increasing lack of clarity and
situational understanding while complexity is associated with large numbers of
richly and dynamically interacting systems and subsystems with behavior difficult
to predict. The concept of emergence is associated with inability to deduce
behavior, structure, or performance from constituent elements while interdependency relates to mutual influence among different complex systems through which
the state of a system influences, and is influenced by, the state of other interconnected systems. The uncertainty aspect of current landscape is associated with
having incomplete knowledge casting doubt for decision/action consequences.
Certainly, these concepts align with the notions of ‘messes’ (Ackoff 1974) and
‘wicked problems’ (Rittel and Webber 1973).
Operating under these conditions is a set of systems “so vital and ubiquitous that
their incapacity or destruction would not only affect the security and social welfare
of any nation, but also cascade across borders” (Gheorghe et al. 2007, p. 6).
Examples of such system include but not limited to chemical industries, communication systems, emergency services, energy, food and agriculture, healthcare and
public health, and transportation systems. Collectively, referred to as critical
infrastructures, research pertaining to such systems tends to “addresses elements of
assessment, remediation, indications and warnings, mitigation, response, and
reconstruction pertaining to hazards, risks, and threats from natural and man-made
events affecting public well-being—public safety, economic vitality, and security”
(Gheorghe and Katina 2014, p. 194).
The importance of critical infrastructures can be highlighted on two fronts: first
is the perspective of the level to which critical infrastructures influence public
well-being. Arguably, all daily activities are influenced by goods and services that
are provided by critical infrastructures: clean water, save food, lighting, banking,
shopping, transportation…the list goes on. Continuous operability and availability
vii
viii
Preface
of critical infrastructure is imperative. Second is the consideration of frequency of
occurrence and increasing loss of lives and property associated with natural and
man-made events. Harmful events, natural or man-made, have always occurred.
However, there has been unprecedented increase in occurrence and causalities
associated with events such as hurricanes and terror attacks. These two fronts
suggest a need for development of methodologies, methods, tools, and techniques
capable of addressing emerging issues. This is not a new insight. In fact, it is widely
accepted that science, state, business, and military have failed to deliver on their
promises of a modern society free of risk (Beck 2006; Escobar 2004). In the context
of critical infrastructures, addressing these issues might require thinking ‘outside
and above’ the box.
These thoughts go hand-in-hand a quote that is often attributed to Albert
Einstein, “We cannot solve our problems with the same level of thinking that
created them.” The same sentiments are echoed by Hammond (2002) who suggests
that “problems confronting humanity at this stage in our history (poverty, violence,
crime, environmental degradation and nuclear weapons…terrorism) are systemic
and cannot be understood or resolved in isolation” (p. 430). When these ideas a
coupled with “dwindling applicability of ‘old’ methods and tools…[the] need to
(re)think such issues as infrastructure protection, deterioration, assessment, remediation, indications and warnings, mitigation, response, and reconstruction”
(Gheorghe and Katina 2014, p. 195) becomes apparent.
Therein these sentiments lay the purpose for the present research—the development of a sound framework for an innovative statistical approach to risk and
vulnerability assessment in the transportation of hazardous materials (i.e., hazmat).
To fulfill this purpose, eight chapters and four appendixes have been carefully
crafted to enable understanding of concepts, ample utility of models, and transferability of the presented research. The intended audience of the book is primarily
practitioners and analysts involved in managing risk associated with transportation
of hazmat. However, business leaders and policy-makers will find this book useful
especially since they are ultimately responsible for decisions involving business
transactions including investment and development of policy the affect public
well-being. Graduate students interested in the present topic may need to ‘pay a
close attention’ to procedures involved in the development of equations and
models.
Chapter 1 introduces the research domain of critical infrastructures along with
the underlying themes from which the need for robust methodologies, methods,
tools, and techniques has sprung. The need for new approaches is made more
apparent in Chap. 2 with a consideration of risk and vulnerability associated with
the transportation of hazmat. Specifically, a new and novel approach, hotspot, is
introduced along with the underpinnings of spatial information and complementary
cumulative distribution function.
Chapter 3 covers methods and corresponding equations related to probability of
occurrence of loss of containment that result in accidents. This chapter includes
detailed accounts on how to identify initiating events in the case of two modes of
transportation: rail and road. Chapter 4 addresses consequences associated with loss
Preface
ix
of containment. Types of consequences are discussed (fire, explosion, and acute
intoxication) along with specific methods for their calculations.
An important aspect of risk is the conceptualization of vulnerability. How though
do we define vulnerability? And more specifically, how can it be quantified for use in
a methodology? Chapter 5 addressed this issue in general and then in the transportation system. Chapter 6 covers two methods that can be used in quantitative
assessment of vulnerability in transportation systems. First is the Index Method
which targets the assessment of the vulnerability level and second is the Matrix
Method which, as the outcome, derives a robustness index. This chapter concludes
with a proposed model for assessing vulnerability of transportation corridors.
Chapter 7 is a continuation of the models introduced in Chap. 6. It covers a
quantitative vulnerability assessment method which models phenomena in
multi-component systems. The first part of this chapter provides foundational
information while the second part provides procedures for application of the
method. The concluding chapter, Chap. 8, is a case application of present research.
A real-world case scenario, a transportation system ‘Aarau-Zurich’ is selected and
analyzed for hotspots.
There are four complementary appendixes; each provide essential information
related to theory, methods, and utility of present research. Appendix A elaborates
on methods and tools for Probabilistic Risk Assessment and Reliability, Availability,
Maintainability and Safety from which master logical diagrams, event tree analysis,
and life data analysis (important tools in present research) are derived. Appendix B
introduces the importance of decision support systems in transportation of hazmat
as well as elaborating on the utility geographical information system in spatial
analysis. Appendix C provides guidelines for developing an integrated software
platform for risk and vulnerability assessment in transportation of hazmat.
A description of a proposed architecture and its constituent blocks is provided along
with potential capabilities. Lastly, Appendix D is designed to offer defensible yet
simplistic explanation of how one arrives at the equation of state of system with
many bi-stable entities—an issue that is rather not easy to understand by any stretch
of imagination.
References
Ackoff, R. L. (1974). Systems, messes, and interactive planning. In Redesigning the future:
Systems approach to societal problems (pp. 20–33). New York, NY: John Wiley & Sons Inc.
Beck, U. (2006). Living in the world risk society. Economy and Society, 35(3), 329–345.
Escobar, A. (2004). Beyond the third world: Imperial globality, global coloniality and
anti-globalisation social movements. Third World Quarterly, 25(1), 207–230.
Gheorghe, A. V., & Katina, P. F. (2014). Editorial: Resiliency and engineering systems—Research
trends and challenges. International Journal of Critical Infrastructures, 10(3/4), 193–199.
Gheorghe, A. V., Masera, M., De Vries, L., Weijnen, M., & Kröger, W. (2007). Critical
infrastructures: The need for international risk governance. International Journal of Critical
Infrastructures, 3(1/2), 3–19.
x
Preface
Hammond, D. (2002). Exploring the genealogy of systems thinking. Systems Research and
Behavioral Science, 19(5), 429–439.
Katina, P. F. (2015). Systems theory-based construct for identifying metasystem pathologies for
complex system governance (Ph.D.). Virginia, USA: Old Dominion University.
Keating, C. B., Katina, P. F., & Bradley, J. M. (2014). Complex system governance: Concept,
challenges, and emerging research. International Journal of System of Systems Engineering, 5
(3), 263–288.
Martin, J. (2006). The meaning of the 21st century: A vital blueprint for ensuring our future. New
York, NY: Riverhead Books.
Rittel, H. W. J., & Webber, M. M. (1973). Dilemmas in a general theory of planning. Policy
Sciences, 4(2), 155–169.
Tainter, J. A. (1988). The collapse of complex societies. New York, NY: Cambridge University
Press.
Acknowledgments
Authors wish to acknowledge different people and organizations involved in the
inception, creation, and the publication of this research. Though too many to
include them on this page, many scientists were consulted in the course of this
work: none more than Prof. Wolfgang Kröger—ETH Zürich, Switzerland; Dr.
Ioannis Papazoglou—National Center for Scientific Research ‘DEMOKRITOS’,
Greece; Adolf Dörig—Dörig + Partner AG, Switzerland; Prof. Radu Cornel—
Politehnica University of Bucharest, Romania; Jürg Birchmeier—Laboratorium fur
Siecherheistanalytik, Switzerland; Dr. Charles Keating—Old Dominion University,
USA; and Dr. Dan Vamanu—‘Horia Hulubei’ National Institute of Physics and
Nuclear Engineering, Romania.
Authors acknowledge support of Integrated Risk Governance Project—
IHDP/Future Earth under grant number: 2010DFB20880, 2012DFG20710.
Finally, authors are thankful to Cynthia Feenstra and Nathalie Jacobs of Springer
Publishing Company for their administrative support in publishing this book.
xi
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . .
1.1 Critical Infrastructures . . . . . . . . . . .
1.2 Major Themes . . . . . . . . . . . . . . . . .
1.3 Transportation of Hazardous Materials
References . . . . . . . . . . . . . . . . . . . . . . .
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2 Risk Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Risk Assessment in Hazmat Transportation . . . . . . . . . . . . . .
2.1.1 The Hot Spots Approach . . . . . . . . . . . . . . . . . . . . .
2.1.2 The Statistical Approach . . . . . . . . . . . . . . . . . . . . .
2.2 Extension of the Risk Assessment Methodology
for Multimodal Transportation . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 The ‘Hot Spot’ Method . . . . . . . . . . . . . . . . . . . . . .
2.2.2 The Statistical Method . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 The Complementary Cumulative Distribution Function
as a Risk Expression of the Health Impact . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Quantitative Probability Assessment of Loc Accident. . . . . . . .
3.1 The Methodology: Loc Accident Probability Computation . .
3.1.1 Tools and Techniques . . . . . . . . . . . . . . . . . . . . . .
3.2 Models and Algorithms: Loc Accident Probability
in Transportation by Rail . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Computational Scheme for LOC Accident by Rail . . .
3.3 Models and Algorithms: Loc Accident Probability
in Transportation By Road . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Deductively Model the Reality—MLD Development
for LOC During Road Transportation. . . . . . . . . . . .
3.3.2 Computational Scheme for LOC Accident by Road . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
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Contents
4 Loc Consequence Assessment . . . . . . . . . . . . . . . . . . . . . .
4.1 Physical to Biological Effects’ Relationship. . . . . . . . . .
4.2 Fire Consequence Assessment . . . . . . . . . . . . . . . . . . .
4.2.1 Pool Fire Consequence Assessment . . . . . . . . . .
4.2.2 Flare Fire Consequence Assessment. . . . . . . . . .
4.2.3 BLEVE Consequence Assessment . . . . . . . . . . .
4.3 Explosion Consequence Assessment. . . . . . . . . . . . . . .
4.3.1 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Acute Intoxication Consequence Assessment . . . . . . . . .
4.4.1 Computing the Risk Radii . . . . . . . . . . . . . . . .
4.4.2 Computing the Lethality Percentage. . . . . . . . . .
4.4.3 An Algorithm for Acute Intoxication Assessment
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 The Vulnerability Issue . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Definitions and Conceptualization . . . . . . . . . . . . . . .
5.2 Methodological Aspects in Quantitative Vulnerability
Assessment in Transport Systems . . . . . . . . . . . . . . .
5.2.1 Transportation System Definition. . . . . . . . . . .
5.2.2 Defining the System by Indicators . . . . . . . . . .
5.2.3 The Vulnerability Assessment of Transportation
System. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Consensus-Driven Models for QVA in Transportation
Corridors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 The Index Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Designing the System . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 The Risk-Management Capability Index and Weights
Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.3 The Index Method: Transportation Corridor Vulnerability
Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 The Relevance Matrices Method . . . . . . . . . . . . . . . . . . . . . .
6.2.1 The Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Transportation Corridor Vulnerability Assessment Model
with the Relevance Matrices Method . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Physical Analogies-Based Model for Quantitative Vulnerability
Assessment of Transportation Corridors . . . . . . . . . . . . . . . . .
7.1 Quantitative Vulnerability Assessment Method; Modeling
Cooperative Phenomena in Multi-component Systems . . . . .
7.1.1 System Description by Indicators. . . . . . . . . . . . . . .
7.1.2 The Control Variables . . . . . . . . . . . . . . . . . . . . . .
7.1.3 System Constituents—System State Space . . . . . . . .
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Contents
xv
7.1.4 Vulnerability Basins—The Instability Region . . .
7.1.5 The Quantitative Vulnerability Assessment . . . . .
7.2 Applying QVA Model for the Vulnerability Assessment
of Transportation Corridors . . . . . . . . . . . . . . . . . . . . .
7.2.1 Indicators Selection . . . . . . . . . . . . . . . . . . . . .
7.2.2 Computing the Physical Indicators—YUi and YVj
7.2.3 Transportation System Vulnerability Assessment .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 An Illustrative Example—The Case for Aarau-Zurich .
8.1 Transportation Description . . . . . . . . . . . . . . . . . .
8.1.1 Graph Coordinate Axis Limits . . . . . . . . . .
8.1.2 Transportation Statistics . . . . . . . . . . . . . . .
8.2 Representation Maps of the Transportation . . . . . . .
8.2.1 ‘Aarau-Zurich’ TRANSPORTATION Map
Representation . . . . . . . . . . . . . . . . . . . . .
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Appendix A: Tools and Techniques for PRA and RAMs: A Primer . . . 177
Appendix B: Design Guidelines for Hazmat Transportation Decision
Support Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Appendix C: Implementation Guideline for Hazmat
Transportation DSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix D: Arriving at Equation for State of a System with many
Bi-stable Entities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Chapter 1
Introduction
Abstract This chapter introduces basic concepts in the field of critical infrastructures. The importance of the field for functionality of modern society is
established in the context of major themes pertinent to the field itself (i.e., risk,
vulnerability, interdependency, and resiliency). A particular sector of interest—
transportation of chemicals (i.e., dangerous goods)—is then introduced to set the
stage for the reminder of present research.
1.1
Critical Infrastructures
There is wide recognition that modern society depends on goods and services
provided by a set of complex systems known as critical infrastructures. These
systems are often referred to as critical because they intrinsically connectedly
maintaining and sustaining public well-being, safety, and economic prosperity
(Gheorghe et al. 2006; Katina and Hester 2013; Kröger and Zio 2011; Rinaldi et al.
2001). At a fundamental level, the domain of critical infrastructures revolves around
chemicals, commercial facilities, communications, critical manufacturing, dams,
defense industrial bases, emergency services, energy, financial, services, food and
agriculture, government facilities, health care and public health, information technology, nuclear reactors, materials, and wastewater systems (Obama 2013).
At first glance, the domain of critical infrastructure (CI) appears to address
sudden and catastrophic infrastructure failures and their impact (Calida and Katina
2012). This is only a partial view of this domain. Basic questions, such as how
infrastructures become critical, what makes a system critical, who is in charge of
such systems, can such systems operate risk-free, and how can policymakers and
researchers use scientific enquiry to protect infrastructures, present a different set of
challenges. Arguably, responses to such basic questions require a different, albeit
holistic, perspective, capable of addressing current societal changes (i.e., rapid
technological changes, socioeconomic factors, policy) and infrastructure complexity involving infrastructure systems as well as their interconnections (Gheorghe
et al. 2006; Katina et al. 2014; Rinaldi et al. 2001).
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_1
1
2
1
Introduction
Table 1.1 A representative set of definitions for ‘critical infrastructures’
Author(s)
CI definition
Clinton (1996,
p. 37347)
Certain national infrastructures are so vital that their incapacity or
destruction would have a debilitating impact on the defense or
economic security of the USA
Critical infrastructures consist of those physical and information
technology facilities, networks, services, and assets which, if
disrupted or destroyed, would have a serious impact on the health,
safety, security, or economic well-being of citizens or the effective
functioning of governments in the Member States
… so vital and ubiquitous that their incapacity or destruction would
not only affect the security and social welfare of any nation, but also
cascade across borders
European
Council (2004, p. 3)
Gheorghe
et al. (2007, p. 6)
Despite relative importance of critical infrastructures, there remains a lack of a
universally accepted worldview on how to define and/or manage infrastructure
systems. Moreover, information and knowledge regarding such infrastructures is
often dispersed across individual infrastructure operators, sometimes with competing objectives. Table 1.1 provides a representation of definitions from various
perspectives.
However, the lack of a universally accepted worldview and dispersed knowledge
bases should not hinder progress. In fact, it has been noted that the different perspectives ‘show the potential sources of divergence in the development of the
[critical infrastructure] field … [with]. Each perspective brings a logic which provides its own internal validation to the community which produces and consumes
the perspective’ (Keating and Katina 2011, p. 240). Katina and Keating’s (2015)
research suggests that there are three diverging perspectives for this field: governmental, industrial (business), and academic. These perspectives are elaborated
upon in Fig. 1.1. It should be obvious that these perspectives do not exist in
Fig. 1.1 Three major perspectives in the field of critical infrastructures, adapted from Katina and
Keating (2015)
1.1 Critical Infrastructures
3
isolation. It can also be noted that the governmental worldview on critical infrastructures tends to influence the industrial and academic worldviews through the
regulation and the setting of funded research priorities especially at the national and
international levels (Moteff 2010).
1.2
Major Themes
The complexity associated with society changes (e.g., moving from public to
private governance policies, rapid technological and institutional changes,
and increasing demand for quality services) sets the stage for need to understand and effectively manage critical infrastructures—especially their services
(Thissen and Herder 2003). In effect, there is a need to ensure that infrastructures
are capable and able to successfully produce their expected outcomes (i.e., products, goods, and services). Successfully producing the desirable outcomes depends
on various factors including infrastructure properties and interrelationships among
infrastructures and how they relate to public well-being (Katina and Pinto 2012;
Katina et al. 2014). Expounding on the need to understand and manage infrastructures are classical themes that set the foundations for research. Table 1.2 provides a set of themes for the field of critical infrastructures.
Certainly, there is a need to make infrastructures more dependable, reliable, and
resilient to natural and man-made hazards, risks, and threats. Moreover, the
increasing occurrence and severity of recent events including the 9/11 attacks,
Hurricane Katrina, 2011 Tōhoku earthquake, Tsunami earthquakes, and countless
cyber attacks seem to indicate that our systems and indeed our modern society are
exposed, fragile, susceptible, and vulnerable to different kinds of hazards, threats,
and risks.
Moreover, if one works with the assumption that the goal of maintaining and
sustaining public health, economy, and security depends on the inputs and outputs
of multiple well-interconnected infrastructure systems, the relationship among
infrastructures cannot be not one to one; rather, it is multidirectional. This multidirectional relationship is a theme in critical infrastructures and is often explored
through the concept of interdependency. The Merriam-Webster Encyclopedic
Dictionary notes that the term ‘interdependency’ is a combination of two distinctive
words: inter and dependency (Merriam-Webster 2006). The prefix inter relates to
among, between, within, and shared. On the other hand, dependency means being
influenced, determined by, conditioned by, or subject to another for support.
Seminal contributions of Rinaldi et al. (2001) have to be recognized when it
comes to the concept of interdependency in critical infrastructures. Rinaldi et al.
posited that infrastructure interdependency is categorized into four types (i.e.,
physical, cyber, geographic, and logical). This work has been expended to include a
mathematical formulation for interdependency (Dudenhoeffer et al. 2006). An even
broader categorization of infrastructure interdependency is provided by Katina et al.
4
1
Introduction
Table 1.2 A set of major themes for the field of critical infrastructures
Major themes in critical
infrastructure
Theme definition
Vulnerability
‘[v]ulnerability is defined as the manifestation of the inherent
states of the system that can be subjected to a natural hazard or be
exploited to adversely affect that system’ (Aven 2011, p. 515).
Since most critical infrastructures operate in the ‘open,’ they are
prone to physical harm (e.g., explosions) and cyber attacks
Operability of an infrastructure may depend on the operations in
other critical infrastructures. This relationship also exists in the
relationship between public well-being and operability of other
infrastructures (e.g., operability of an electrical grid for electricity
provision)
As used in this research, relates to concepts of dose amount,
pollution, toxicity, and surface area (Gheorghe 2005). When used
in terms of critical infrastructure, it explains proximity such as
being exposed to natural threat (e.g., a hurricane) and man-made
cyber threats, for example, via ubiquitous computing and
telecommunications that could be hacked
A fragile defines a condition of being easily broken down. In the
area of power plants, fragility is ‘the likelihood of failure as a
function of peak ground acceleration for plant structures,
equipment, and other components’ (Kaplan et al. 1983, p. 171).
The concern for the field of critical infrastructure is the
identification of those systems that are fragile, understanding how
fragile they are and developing means to address and possibly
reduce the fragility
Blanchard and Fabrycky (2006, p. 369) define reliability as ‘the
ability of a system to perform its intended mission when
operating for a designated period of time, or through a planned
mission scenario (or series of scenarios), in a realistic operational
environment.’ From the critical infrastructure perspective,
reliability entails ensuring that infrastructure systems can produce
their intended good and serves when needed, despite conditions
that may hinder their reliability
Risk is usually defined in terms of probability of occurrence of an
event and magnitude of the resulting consequences (ASCE 2009).
Given the importance of critical infrastructures, it is only natural
to consider probabilities that certain events (e.g., loss of a
containment) may occur and the resulting consequences on
different levels (e.g., public well-being, business operations,
environment)
Critical infrastructures face many natural events (e.g., power
outage due to storms) and man-made events (e.g., power outage
due to sabotage), and therefore, their operability can be expected
to be impacted. The key, however, is ensuring that infrastructures
have the ability to quickly bounce back after failures since
prolonged failures can have debilitating impact on society
(Gheorghe and Katina 2014)
Dependency
Exposure
Fragility
Reliability
Risk
Resiliency
1.2 Major Themes
5
Table 1.3 Types of critical infrastructure interdependencies
Type of interdependency
Definition
Physical interdependency
Exists between infrastructure systems if the state of
infrastructure depends on the outputs (i.e., product, goods, and
services) of another infrastructure. In Rinaldi et al. (2001,
p. 15), it is demonstrated that the physical interdependency in
infrastructures ‘arises from the physical linkage between the
inputs and outputs of two agents [where the] commodity
produced or modified by one infrastructure (an output) is
required by another infrastructure for it to operate (an input).’
Exists among infrastructure systems if the functioning of an
infrastructure and its components depends on the output that is
transmitted via information and telecommunication systems.
Rinaldi (2004, p. 2) notes that ‘computerization and automation
of modern infrastructures and widespread use of SCADA
systems have led to pervasive cyber interdependencies.’
Exists among infrastructure systems if ‘infrastructure
components, e.g., transmission lines, water pipelines, gas
pipelines, and telecommunications cables share common
corridors’ (GITA 2008, p. 3). Common corridors are needed in
the coupling of infrastructure components; however, this poses
a threat to all interdependent infrastructure systems in case of
failure stemming from explosion
According to Rinaldi (2004, p. 2), logical interdependency
exists in infrastructures ‘if the state of each [infrastructure]
depends upon the state of the other [infrastructure] via some
mechanism that is not a physical, cyber, or geographic
connection.’ A good example is regulatory stipulations that
linked the California power crisis and financial infrastructure
(Sweeney 2002)
This interdependence becomes apparent only after an event
happens. For example, after the attacks on the World Trade
Towers, US government issued certain regulations that affected
all US air transport systems. And the flying experience was
forever changed (Mendonca and Wallace 2006)
Refers to interdependency that exists due to public opinion,
confidence, fear, and a culture as a whole as a result of
infrastructure or component failure. Consider the restoration of
air service after the events of 9/11. Air traffic was reduced due
to the public’s evaluation of travel safety resulting in job cuts
and bankruptcies (Dudenhoeffer et al. 2006)
Cyber interdependency
Geographic
interdependency
Logical interdependency
Policy and/or procedural
interdependency
Societal interdependency
(2014) with applications in health care. Table 1.3 provides a summary of types of
interdependences.
Research into infrastructure interdependencies can be instrumental in understanding how outputs of a given infrastructure can affect the operability of the other
infrastructure. This type of analysis can be useful in developing prevention, mitigation, and recovery measures. Whether one is interested in interdependencies or
any other theme of this field, it is certainly clear that there is an urgent need for the
6
1
Introduction
development of robust methodologies, methods, tools, and techniques that can be
used to address different issues in the field of critical infrastructures.
A particular issue of interest for current research efforts is chemicals, more
specifically the transportation of chemical, thereafter known as dangerous goods.
1.3
Transportation of Hazardous Materials
The chemical industry plays a key role on public well-being. This sector is comprised of companies that produce industrial-level chemicals, and these chemicals
are used in many aspects of human life including processing of oil, natural gas, air,
water, metals, and minerals into usable products. In the context of critical infrastructures, the chemical sector has been identified as an integral component to
economy, relying on and supporting a wide range of other critical infrastructure
sectors (USDHS 2013).
According to the US Department of Homeland Security,1 this sector can be
divided into five main segments of basic chemicals, specialty chemicals, agricultural chemicals, pharmaceuticals, and consumer products. As expected, each
segment has a distinctive set of characteristics, growth dynamics, markets, new
developments, and issues (i.e., risk) which are beyond the scope of current discussion. However, current efforts are dedicated toward risk associated with the
transportation of such goods.
Transportation simply refers to means of conveyance or travel from one place to
another. In the context of chemical, it refers to moving chemical from one location
to another. This movement can be done via several mechanisms as indicated in
Table 1.4.
Certainly, the role of transportation system within the context of movement of
dangerous goods is to ensure quick, safe, and secure movement of goods and
people through streets, towns, regions, and countries overland, sea, or air. However,
this is not a simple task as illustrated by accidents involving dangerous goods and
their impact on people and the environment. In fact, dangers associated with
transporting hazardous materials are all too common (NTSB 2009). One of the most
recent examples is the Lac-Mégantic derailment that took place at Lac-Mégantic,
Quebec, Canada in July 2013 in which forty-seven (47) people died when there was
a derailment of an oil shipment train. The oil shipment caught fire, exploded, and
destroyed more than thirty buildings. It goes without mentioning the mental effects
and environmental effects of the derailment (Becker et al. 2000). Such kind of
events, together with the need to prevent spills and illegal dumping of chemicals, were instrumental in pushing toward regulations. One such regulation was the
enactment of the Hazardous Materials Transportation Act (HMTA) in 1970s with
the purpose to ‘protect against the risks to life, property, and the environment that
1
http://www.dhs.gov/chemical-sector#.
1.3 Transportation of Hazardous Materials
7
Table 1.4 Forms of modes within the transportation sector
Modes of transportation
Description of modes of transportation
Aviation
A mode of transportation that includes aircraft, air traffic control
systems, and thousands of airports, heliports, and landing strips.
This mode includes civil and joint-use military airports,
heliports, short takeoff and landing ports, and seaplane bases
It encompasses millions miles of roadways, bridges, and
tunnels. Vehicles (i.e., automobiles, motorcycles, trucks, and
commercial freight vehicles) use these while carrying hazardous
materials
It consists of miles of coastline, ports, waterways, square miles
of Exclusive Economic Zone, and intermodal landside
connections, which allow the various modes of transportation to
move people and goods to, from, and on the water
This mode consists of service by buses, rail transit (commuter
rail, heavy rail—also known as subways or metros—and light
rail, including trolleys and streetcars), long-distance rail, and
others (e.g., cable cars, inclined planes, funiculars, and
automated guideway systems)
This mode consists of vast networks of pipeline that traverse
hundreds of thousands of miles throughout countries carrying
natural gas and other hazardous liquids
This mode consists of major carriers, hundreds of smaller
railroads, miles of active railroad, freight cars, and locomotives
This mode moves millions of messages, products, and financial
transactions each day. This mode of transportation is
distinguished by its focus on letter or flat mail, publications, or
small- and medium-sized packages and by service
Highway infrastructure and
motor carrier
Maritime transportation
system
Mass transit and passenger
rail
Pipeline systems
Freight rail
Postal and shipping
are inherent in the transportation of hazardous material in intrastate, interstate, and
foreign commerce’ (USSoT 1978, p. 131).
In the present research, emphasis is placed on risk and vulnerability associated
with the transportation of dangerous goods by rail and road.
References
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Society of Civil Engineers.
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Becker, S. M., Pitt, R., & Clark, S. (2000). Environmental health, public safety, and social impact
associated with transportation accidents involving hazardous substances. Tuscaloosa, AL:
University Transportation Center for Alabama.
Blanchard, B. S., & Fabrycky, W. J. (2006). Systems engineering and analysis (4th ed.). Upper
Saddle River, NJ: Pearson-Prentice Hall.
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Calida, B. Y., & Katina, P. F. (2012). Regional industries as critical infrastructures: A tale of two
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Gheorghe, A. V. (2005). Integrated risk and vulnerability management assisted by decision
support systems: Relevance and impact on governance (Vol. 8). Dordrecht, The Netherlands:
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Gheorghe, A. V., & Katina, P. F. (2014). Editorial: Resiliency and engineering systems—research
trends and challenges. International Journal of Critical Infrastructures, 10(3/4), 193–199.
Gheorghe, A. V., Masera, M., De Vries, L., Weijnen, M., & Kröger, W. (2007). Critical
infrastructures: The need for international risk governance. International Journal of Critical
Infrastructures, 3(1/2), 3–19.
Gheorghe, A. V., Masera, M., Weijnen, M. P. C., & De Vries, J. L. (Eds.). (2006). Critical
infrastructures at risk: Securing the European electric power system (Vol. 9). Dordrecht, The
Netherlands: Springer.
GITA. (2008). The geospatial dimensions of critical infrastructure and emergency response:
White paper series (p. 9). Aurora, CO: Geospatial Information and Technology Association.
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Interdependencies.pdf
Kaplan, S., Perla, H. F., & Bley, D. C. (1983). A methodology for seismic risk analysis of nuclear
power plants. Risk Analysis, 3(3), 169–180. doi: http://doi.org/10.1111/j.1539-6924.1983.
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Katina, P. F., & Hester, P. T. (2013). Systemic determination of infrastructure criticality.
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Katina, P. F., & Keating, C. B. (2015). Critical infrastructures: A perspective from systems of
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Katina, P. F., & Pinto, C. A. (2012). On critical infrastructure interdependency. In The 33rd
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with applications to healthcare. International Journal of Critical Infrastructure Protection, 7
(1), 12–26.
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York city critical infrastructures. Journal of Infrastructure Systems, 12(4), 260–270.
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Federal Street Press.
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Washington, DC: Congressional Research Service.
NTSB. (2009). Cargo hose rupture and release of anhydrous ammonia during offloading of a
Werner transportation services cargo tank motor vehicle at the tanner industries plant:
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National Transportation Safety Board.
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Obama, B. H. (2013). Critical infrastructure security and resilience. Washington, D.C.: The White
House. Retrieved from http://www.fas.org/irp/offdocs/ppd/ppd-21.pdf
Rinaldi, S. M. (2004). Modeling and simulating critical infrastructures and their interdependencies.
In Proceedings of the 37th Hawaii International Conference on System Sciences (pp. 1–8). Big
Island, Hawaii. http://doi.org/10.1109/HICSS.2004.1265180
Rinaldi, S. M., Peerenboom, J. P., & Kelly, T. K. (2001). Identifying, understanding, and
analyzing critical infrastructure interdependencies. IEEE Control Systems, 21(6), 11–25. doi:
http://doi.org/10.1109/37.969131
Sweeney, J. L. (2002). The California electricity crisis. Stanford, CA: Hoover Institution Press.
Thissen, W. A., & Herder, P. M. (2003). Critical infrastructures: State of the art in research and
application. Boston, MA: Kluwer Academic Publishers. Retrieved from http://www.loc.gov/
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http://www.gpo.gov/fdsys/pkg/USCODE-2010-title49/content-detail.html
Chapter 2
Risk Assessment
Abstract There is no one widely accepted definition of risk. In fact, the meaning of
the term risk is widely debated in literature (Holton 2004; Knight in Risk, uncertainty, and profit. Hart, Schaffner & Marx; Houghton Mifflin Co. Boston, MA,
1921). However, risk is usually associated with uncertainty. In terms of system life
cycle, risk is associated with uncertainty and opportunities related to cost, schedule,
and performance (INCOSE in Systems engineering handbook: a guide for system
life cycle processes and activities. INCOSE, San Diego, CA, 2011). In the area of
decision making, risk is associated with probabilities of unknown outcomes
(Gibson et al. in How to do systems analysis. Wiley-Interscience, Hoboken, NJ,
2007). Nonetheless, a classical view of risk considers probability of occurrence of
an event that could halt operations and consequences of such an event (ASCE in
Guiding Principles for the Nation’s Critical Infrastructure. American Society of
Civil Engineers, Reston, VA, 2009). The comprehensive analysis which consists of
an objective evaluation of risk in which assumptions and uncertainties are clearly
considered and presented is referred to as risk assessment. Risk assessment involves
the determination of quantitative or qualitative estimation of risk related to a
concrete situation and a recognized threat or hazard.
2.1
Risk Assessment in Hazmat Transportation
In the particular case of risk assessment in the transportation of hazardous (i.e. hazmat)
materials, the calculations of probability of occurrence of the disruptive event (the loss
of containment) and of the consequences of such event (the impact on the public and
the environment) play a critical role. Risk assessment typically is the basis for concepts of risk classifications (e.g., acceptable–unacceptable) and is instrumental in
areas of decision making, resource allocation, and policy change. There are several
methods for risk assessment that may differ from industry to industry, especially based
on the type of risk involved (e.g., environmental, ecological, and public health). Some
domains (e.g., nuclear, aerospace, oil, rail, and military) have a long standing in the
concept of risk, and their risk assessment methods tend to be more advanced.
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_2
11
12
2 Risk Assessment
Fig. 1 The concept of impact
location and affected area
Risk assessment in hazmat is unique; an incident involving a transportation
mode (e.g., vehicle or train) carrying hazmat cargo can produce undesirable shortand long-term effects on human health, environment, and property because of the
possible release of toxic material and effects can be felt beyond an immediate area
of an accident. Figure 2.1 attempts to illustrate this point by indicating that effects
on an accident can be felt beyond the location of an impact. The impact location is
the point of an accident and is represented by the center of the circle. From this
simple illustration, the relevance of including spatial data and properties of a
hazmat starts to become evident. Moreover, research suggested that 87 % of
reported accidents (Major Hazard Incident Data Service—a major database)
involve release hazmat (Oggero et al. 2006). Indeed, a hazmat event could be
referred to as Low Probability High Consequence.
2.1.1
The Hot Spots Approach
In many models, risk is computed without considering spatial information which
characterizes transportation routes. This issue can be addressed through a consideration of hot spots (Gheorghe et al. 2003, 2005; Riegel 2015). The concept of ‘hot
spots’ introduces route spatial characteristics and influences the computation of the
probability and consequence assessment in the case of a loss of containment (LOC)
accident (Gheorghe et al. 2003). The hot spots method is a practical and intuitive
solution for developing accident scenarios based on a more detailed characterization
of the determining risk factors that can be encountered along a transportation route
(Gheorghe et al. 2004). The relationship between LOC probability, LOC consequence, and risk is presented in Fig. 2.2. When the concept of hot spots is deployed,
several measures that would be ignored during a traditional approach are brought at
the forefront of the analysis. In the case of transportation, especially land transportation, a logical conjugation of one hot spot might be defined in terms of a set of
predefined criteria. This criterion might involve:
• The existence of at least one of the sensitive infrastructure components, and/or
• Crossing a given type of land use, and/or
2.1 Risk Assessment in Hazmat Transportation
13
Fig. 2 Relationship between probability, consequence, and risk
• Population density which could be indicated in terms of excess of a given
threshold.
The sensitive infrastructure components can be identified based on road and rail
accident statistics. This approach leads to the identification of the most frequent spatial
characteristics in the proximity of the accidents. Identified ‘sensitive’ infrastructure
components include the following: motorway rest areas, motorway entrance/exits,
bridges, passages, tunnels, high-voltage line crossings, crossings, traffic jam areas,
sharp curves areas and gas stations for road transportation, and station, signal, switch,
bridge, passage and tunnels for rail transportation, respectively (Gheorghe et al. 2003).
The hot spots approach allows the multicriteria risk characterization of the
transportation routes, by taking into account the risk contributing factors given by
14
2 Risk Assessment
the infrastructure, environment, and population. The first step in applying this
method is identifying the areas along the route where the definition criteria of a hot
spot are met. In this case, a route is described by a list of hot spots (i.e., locations
with a higher risk of accidents). The second phase involves performing statistics in
every hot spot, over a circular area determined by a relevant radius that equals the
relevant radius of the considered physical effect (e.g., relevant radius for BLEVE—
boiling liquid expanding vapor explosion). The gathered data are the basis for a hot
spot risk index. Finally, the hot spots are then sorted by the risk indices and placed
in risk basins defined in accordance with the risk perception of the analyst.
2.1.1.1
Representing Risk in the Hot Spot Method: The Risk Matrix
The assessment of the hot spots on a transportation segment leads to the creation of
segment risk report (i.e., a listing of critical points along a given segment). A risk
report is a source of the segment’s risk pattern which is a holistic representation of
the risk associated with the analyzed segment. Creating a risk pattern is a two-step
process which involves: (1) sorting and classifying the hot spots as either hot,
warm, or acceptable and (2) building a risk matrix.
Sorting and classifying is done through (a) the characteristic probability of LOC
accident and (b) the consequence assessment which is defined in terms of health
impact quantified by the number of deaths as a result of an accident at the particular
hot spot. A classification of a hot spot (i.e., hot, warm, and acceptable) is done by
setting the threshold values for both probability and lethality. These values are a
reflection of the risk perception by the analyst which is in accordance with previous
research (Clemson 1984; Katina 2015; Quade 1980; Warfield 1976). In the second
step, the building of a risk matrix is done through probability against consequence
measure and populating it with the identified hot spots. This creates an interval
classification of the probabilities and consequences which is conducive in effect
in defining three risk basins within the risk matrix.
2.1.2
The Statistical Approach
2.1.2.1
The Framework
The framework starts from an innovative statistical approach which was introduced
in Gheorghe et al. (2000). The method was originally developed for risk assessment
of hazmat transportation by rail. The validity of the model in the road transportation
case, as well as its potential applicability in other transportation domains, such as
inland waters, has been confirmed in different quantitative assessments undertaken
at the Swiss Federal Institute of Technology (ETH Zürich), Zurich, Switzerland.
This model targets the representation of the risk associated with an activity by
the cumulative frequency of the consequence indicators. In the case of transportation of hazardous materials, this is referred to as the representation of hazmat
2.1 Risk Assessment in Hazmat Transportation
15
transportation by the cumulative frequency of fatalities (CFF). This model requires
an intensive use of the hot spots method in conjunction with a circumstantial
database for statistical analysis of the transportation segment vicinity. The process
of computing the CCF involves:
(a) the identification of the route characteristic hot spots,
(b) setting up a complex source term containing a complete set of scenarios
corresponding to different substance components of the transportation and
distinct release classes (from small to complete release), and
(c) health and environmental impact assessment (in the form of cadastral statistics) accompanied by the LOC probability assessment for each of the plausible
scenarios.
The following section elaborates on the model. Appendix C elaborates on need
for hazmat database development and provides development guidelines.
2.1.2.2
The Statistical Method
This section elaborates on the nature of the problem statement along with the
conceptual aspects and the computational algorithm for obtaining the cumulative
frequency of fatalities (CFF). Note that the objective of the assessment is the
computation of the CFF. Risk associated with a given transport system is then
characterized by the complementary CCFF which is closely related to CCDT—
complementary cumulative distribution function.
The Scenarios
For a given case, the following holds:
• CFF refers to a set of N scenarios
• One scenario is characterized by:
– The substance: A subject of transportation and LOC accident. Each substance is in turn characterized by a vector of physical and chemical properties. These are necessary for the consequence assessment phase.
– One release category: A classification of small, medium, large, and the
corresponding quantities such as kilogram (kg).
– One physical effect: These can include, among others, pool fire, BLEVE, and
toxicity along with the consideration of the physical effects of the substance.
Each of the identified possible effects is then assessed using a corresponding
method of consequence assessment. The results are provided in: (i) Lethality
Percentage as function of Distance and (ii) the characteristic effect radius—
the distance up to which the lethality percentage exceeds zero (0).
– A list of hot spots along a given route is always identified using the hot spots
approach.
16
2 Risk Assessment
Fig. 3 An example of a cumulative fatalities function constructed from NFj and SFj
Obtaining the CFF based on a scenarios set
To construct the CFF, one has to compute for each scenario j (j ¼ 1. . .N, N—
number of scenarios) the two variables:
1. the expected number of fatalities, ðNFj Þ and
2. the expected frequency of occurrence, ðSFj Þ;
If NFj and SFj are known, we proceed by:
– building the NFSF matrix ðNFSF 2 <Nx2 Þ as having NFj and SFj as columns.
That is,
NFSFðj; 1Þ ¼ NFj and NFSFðj; 2Þ ¼ SFj
– sorting the NFSF descending by NFj
– computing the cumulative frequency for each scenario as
CFFðiÞ
i
X
SFj
ð2:1Þ
j¼1
– Build an X–Y diagram as lgðCFFj Þ versus lgðNFj Þ, j ¼ 1. . .N. The polyline
as indicated in Fig. 2.3 is thus obtained using the statistical method.
The Process
Phase 1: Identification of hot spots and the statistics
This phase implies the identification of the hot spots along a given transportation
segment and the computation of the corresponding NF and SF values. Once a hot
spot (i.e. a location along the route which meet the hot spot defintion criteria) is
identified, NF and SF are computed using the following scheme:
1. for each point p of the circular area centered at the hot spot location and having a
radius equal to a given scenario’s characteristic effect radius:
(a) get the distance, d, from the hot spot to point p;
2.1 Risk Assessment in Hazmat Transportation
17
(b) get the expected lethality percentage at distance d by interpolating the scenario characteristic lethality percentage using distance correlation table;
(c) get the expected number of fatalities from the lethality percentage and the
effective number of individuals exposed.
2. compute the expected number of fatalities at hot spot i ðNFi Þ by summing up the
partial results obtained above;
3. the hot spot characteristic LOC frequency is computed by multiplying the
scenario characteristic frequency with the corresponding value from the LOC
probability pattern (LCPP) matrix. The LCPP expresses the assumption that the
LOC event is influenced by the combination of a given land use and the type of
infrastructure (i.e., object/objects) at the hot spot location. The values of LCPP
are assumed a priori and can be obtained from accident statistics and/or using
expert judgment.
Phase 2: Lethality number mitigation factors
It has been shown that models tend to provide over-conservative results especially
when it comes to number of fatalities that could result from a LOC accident
(Vamanu 2006). In reality, however, there are numerous factors that could contribute to mitigating the effects of LOC. For example, if one is considering the
lethality number caused by heat radiation, one can easily notice that the number of
casualties is significantly higher when the scenario accident occurs in open space as
opposed to a residential area. The value of lethality is reduced since there is a
shielding effect that is attributed to the presence of buildings. However, if the same
event takes place in an industrial area, the lethality number could be higher because
of a possible domino effect.
In this case, the statistical method provides several means of tuning up the
assessment in order to reflect this logic. This is done through a consideration of:
Angular sectors mitigation factors
In the case of fire and explosion, it is natural to assume that the effects will spread
into a circular motion. However, this is not plausible when one considers toxicity
because of atmospheric dispersion. Thus, one can reasonably conclude that wind
direction plays a significant role in the validity of the assessment. The wind
direction is taken into account using the following approach: Split the circular area
centered at the accident location in a number m (e.g., ðm ¼ 16Þ of angular sectors,
Sm . Each sector ðSi Þ is given a weight ðwi Þ in accordance with the percentage of the
time the wind blows in the direction within the Si boundaries. The adjusted number
of fatalities would then be given by:
NF ¼
m
X
NFi wi
i¼1
where NFi is the number of fatalities in sector i.
ð2:2Þ
18
2 Risk Assessment
Source term aggravation/mitigation factors
These factors adjust the scenario characteristic effect radius. These factors are
defined taking into account the substance and its mass quantity.
Circumstantial aggravation/mitigation factors
These factors adjust the lethality number provided by the analytical models. The
factors are a defined function of:
– the land-use characteristics (e.g., the presence in the vicinity of flammable
objects as opposed with the presence of fire proof materials);
– the daytime period (e.g., rush hour as opposed to night time);
– the weather; and
– the physical effects.
2.2
Extension of the Risk Assessment Methodology
for Multimodal Transportation
Fundamentally, hazmat transportation for rail and road transportation can be treated
separately. This is primarily due to differences in the mechanics of occurrence of a
LOC accident. However, for a holistic risk assessment, an extension of the
assessment methodology is required to enable coping with complex transportation
schemes which might involve different segments and conditions (Gheorghe et al.
2006).
2.2.1
The ‘Hot Spot’ Method
The way the risk matrix is generated in the case of a singular transportation segment
can be extended for assessing transportation routes and corridors. In this case, a
route is defined as a sequence of continuous transportation segments along which
the transportation may be performed in a multimodal way (either by rail or by road)
and in different circumstances (i.e., different model variables). A transportation
corridor is defined as a collection of routes, potentially disjoined, that form a
fascicle of transportation routes.
An individual assessment of transportation routes yields a set of route characterization reports. When the ‘hot spot’ methodology is applied to each of the
constituent segments, followed by grouping the individual results into a report, and
development of a comprehensive risk matrix, one gets the risk configuration
associated with the route and or the corridor, respectively. The following observations can be made: First, the practical implementation of such an approach comes
with considerable challenges associated with managing high volumes of data.
2.2 Extension of the Risk Assessment Methodology …
19
Second, it is obvious that in the case of partially overlapping routes and corridors
the location of some of the hot spots will be the same. This is determined through
the hot spot definition criteria. In such a case, it is possible to have unfeasible results
especially if there is always a consideration of the common hot spots each time they
appear in different routes. A solution to this issue is to give the analyst the freedom
to choose a representative hot spot, in accordance with analyst’s risk perception.
Third, it is essential to consider hot spot cases in which there is a shared location but
belonging to different transportation segments (e.g., rail and road). In such a case,
both hot spots need to be taken into consideration.
2.2.2
The Statistical Method
Extending the statistical method for the multimodal case implies extending statistical method for transportation routes and statistical method for transportation
corridors. Statistical method for transportation routes involves the following:
1. Building the NFSF matrix for each constituent segment of the route,
2. Centralizing the NFSF matrices into a route characteristic matrix NFSF_route,
3. Computing the CFF for NFSF_route.
Thus, one gets the CFF profile characteristic to the transportation route. The
statistical method for transportation corridors involves the following:
1. Building the NFSF_route matrix for each constituent route of the corridor,
2. Centralizing the NFSF matrices into a corridor characteristic matrix
NFSF_corridor,
3. Computing the CFF for NFSF_corridor.
For managing the hot spots shared by different segments or routes, the same
rules as in the case of the multimodal hot spots assessment should be followed.
2.2.3
The Complementary Cumulative Distribution
Function as a Risk Expression of the Health Impact
Another way of processing the lethality percentage so as to lead to a risk-specific
representation is the complementary cumulative distribution function (CCDF). The
algorithm for CCDF can be sketched as follows (Gheorghe et al. 2003). It is
assumed that the probability of one individual located at distance x from the event
to be affected by the event is equal to the percentage (perc.) of affected people
(resulted from the consequence assessment) divided by 100.
20
2 Risk Assessment
Every perc. value obtained as function of distance is then normalized to the sum
of all of the percentages, thus obtaining the probability distribution function. The
following equations hold:
RX
max
f ðRÞ ¼ 1
ð2:3Þ
Rmin
with f ðRÞ the nominalized perc. The cumulative distribution function is then
computed as follows:
CCDFðRÞ ¼
R
X
f ðRÞ
ð2:4Þ
Rmin
Equation (2.4) leads at the complementary cumulative function defined as
follows:
CCDFðRÞ ¼ 1 CDFðRÞ
ð2:5Þ
References
ASCE. (2009). Guiding principles for the nation’s critical infrastructure. Reston, VA: American
Society of Civil Engineers.
Clemson, B. (1984). Cybernetics: A new management tool. Tunbridge Wells, Kent, UK: Abacus
Press.
Gheorghe, A. V., Birchmeier, J., Kröger, W., & Vamanu, D. V. (2003). Hot spot based risk
assessment for transportation dangerous goods by railway: Implementation within a software
platform. In Proceedings of the Third International Safety and Reliability Conference
(KONBIN 2003), Gdynia, Poland.
Gheorghe, A. V., Birchmeier, J., Kröger, W., Vamanu, D. V., & Vamanu, B. (2004). Advanced
spatial modelling for risk analysis of transportation dangerous goods. In C. Spitzer,
U. Schmocker, & V. N. Dang (Eds.), Probabilistic safety assessment and management
(pp. 2499–2504). London, UK: Springer London. Retrieved from http://link.springer.com/
chapter/10.1007/978-0-85729-410-4_401
Gheorghe, A. V., Birchmeier, J., Vamanu, D., Papazoglou, I., & Kröger, W. (2005).
Comprehensive risk assessment for rail transportation of dangerous goods: A validated
platform for decision support. Reliability Engineering & System Safety, 88(3), 247–272. http://
doi.org/10.1016/j.ress.2004.07.017
Gheorghe, A. V., Grote, G., Kogelschatz, D., Fenner, K., Harder, A., Moresi, E., et al. (2000).
Integrated risk assessment, transportation of dangerous goods: Case study. Zurich,
Switzerland: Target: Basel-Zurich/VCL. ETH KOVERS.
Gheorghe, A. V., Masera, M., Weijnen, M. P. C., & De Vries, J. L. (Eds.). (2006). Critical
infrastructures at risk: Securing the European electric power system (Vol. 9). Dordrecht, the
Netherlands: Springer.
Gibson, J. E., Scherer, W. T., & Gibson, W. F. (2007). How to do systems analysis. Hoboken, NJ:
Wiley-Interscience.
Holton, G. A. (2004). Defining Risk. Financial Analysts Journal, 60(6), 19–25.
References
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INCOSE. (2011) In H. Cecilia (Ed.) Systems engineering handbook: A guide for system life cycle
processes and activities (3.2 ed.). San Diego, CA: INCOSE.
Katina, P. F. (2015). Systems theory-based construct for identifying metasystem pathologies for
complex system governance (Ph.D., Old Dominion University, United States, Virginia).
Knight, F. H. (1921). Risk, uncertainty, and profit. Boston, MA: Hart, Schaffner & Marx;
Houghton Mifflin Co.
Oggero, A., Darbra, R. M., Muñoz, M., Planas, E., & Casal, J. (2006). A survey of accidents
occurring during the transport of hazardous substances by road and rail. Journal of Hazardous
Materials, 133(1–3), 1–7. http://doi.org/10.1016/j.jhazmat.2005.05.053
Quade, E. S. (1980). Pitfalls in formulation and modeling. In G. Majone & E. S. Quade (Eds.),
Pitfalls of analysis (Vol. 8, pp. 23–43). Chichester, England: Wiley-Interscience.
Riegel, C. (2015). Spatial criticality—identifying CIP hot-spots for German regional planning.
International Journal of Critical Infrastructures, 11(3), 265–277. http://doi.org/10.1504/IJCIS.
2015.072157
Vamanu, B. I. (2006). Managementul riscurilor privind transportul substanţelor periculoase:
aplicaţii ale sistemelor dinamice complexe (Dissertation, Universitatea Politehnica Bucureşti,
Facultatea de Chimie Aplicată şi Ştiinţa Materialelor, Catedra de Inginerie Economică,
Bucureşti).
Warfield, J. N. (1976). Societal systems: Planning, policy and complexity. New York, NY:
Wiley-Interscience.
Chapter 3
Quantitative Probability Assessment
of Loc Accident
Abstract The purpose of this chapter is to cover a set of methods and corresponding equations related to the probability of occurrence of loss of containment
(LOC) resulting in accidents. Rail and road transportation cases are addressed. The
methods lay on a practical approach that entails the identification of the initial
sources that in conjunction with known failures of the rolling stock and actions of
the human operator may lead the system to a potentially disruptive state, hence the
loss of containment.
3.1
The Methodology: Loc Accident Probability
Computation
In the context of current research, models can be used to support risk assessment,
particularly during the identification and development of accident scenarios and the
corresponding mitigation procedures. However, assessment needs to be sensitive
enough to account for the characteristics of a given location. The sensitivity aspect
of a model is a relevant issue since the variation of the geomorphological characteristics (e.g., population distribution, land use, and road/railway quality), along a
transportation segment, plays a key role in the overall probability of accident as
well as LOC.
The development of the quantitative probability of LOC models can follow a
detailed logic modeling philosophy—a top-down logical development and/or
bottom-up quantitative modeling. In this research, a top-down approach is adopted
for analyzing the process (LOC accident in rail/road transportation) in terms of
mechanisms of occurrence including segregated initial events. Next, scenario-based
logic and/or statistical models are developed for each of the initial events to perform
the probability computation. The discrete results are then mathematically integrated
from the bottoms-up to produce the LOC event probability. In essence, both
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_3
23
24
3 Quantitative Probability Assessment of Loc Accident
deductive and inductive system analysis techniques are adopted for logical modeling of the transportation system. Under a deductive approach, it is postulated that
the system is already in a failure state (i.e., LOC has occurred) and that the effort is
driven toward finding out possible causes and behavior that might have contributed
to the current state of the system. Accident investigations are typically analyzed
using deductive analyses (Gheorghe et al. 2004). Inductive assessment involves
nominating an initial fault or condition and then asserting the possible effects of the
initial fault on system operation or state. Consequently, deductive methods are
suitable to determine ‘how’ a failed state of a system can occur, while inductive
methods are applied when one is interested in finding out system failure possible
states. In essence, using a deductive model, one finds a response to the question:
how did the system get here? An inductive method provides a response to the
question: what happens to the system if…?
Prior to proceeding to an overview of the modeling and assessment techniques, it
is important to recognize the concept of failure and success spaces in system
operation analysis (Gheorghe et al. 2004). The operation of a system can be considered from two perspectives: the various ways for system success and various
ways for system failure. An enumeration based on these perspectives would provide
a total number of successful system operations, failure system operations, and the
intermediate conditions. Figure 3.1 represents the concept of failure and success
space concepts as adapted from Gheorghe et al. (2004). The set of all system
operation states is called either success or failure space, depending on the perspective of the analysis. At first glance, both approaches appear equivalent.
However, adopting the failure approach is recommended from analytical and ease
of implementation standpoints since (Gheorghe et al. 2004):
• It is generally easier to reach consensus on what constitutes failure than what
constitutes success;
• The failure events are usually discrete events (e.g., ‘tire explodes’), whereas the
success events are characterized by continuous variables;
Fig. 3.1 The concept of failure/success
3.1 The Methodology: Loc Accident Probability Computation
25
• There are more ways to success than to failure, which implies a higher population number in the success space which, in turn, is reflected in both the
development phase and the practicality of the model;
• Mathematics considerations: Most success probabilities are close to 1.0, which
increases the probabilistic calculus complexity.
Failure space perspective is selected for current efforts. This is attributed to the
nature of the task as well as reasons that have been discussed.
3.1.1
Tools and Techniques
This section provides an overview and short introduction to the main modeling and
analytical tools and techniques that will be used in developing the models for LOC
probability assessment. These techniques mainly originate from the engineering
paradigms of probabilistic risk assessment (PRA) and reliability, availability,
maintainability, and safety (RAMS) engineering paradigms. More information
regarding PRA and RAMS is provided in Appendix A.
In current efforts, the master logic diagram (MLD) in failure space technique is
adopted for describing the mechanisms of LOC following an accident and identification of the initial disruptive events (Gheorghe et al. 2006). Moreover, by reading
the MLD, the reader will be introduced to the core assumptions of the LOC accident
models.
Development of the MLD for LOC accidents may be sketched out as follows:
Starting from one undesired event (the LOC), a diagram is developed level by level
through decomposition events and the corresponding contributing subevents, down
to the initiating events. This leads to the identification of the immediate causes that
may lead to the top events which are placed at the bottom level of the MLD. The
analysis of the resulting combinations provides a way to determine different failure
states of the system, as well as the failure sequence that leads to those states.
Event tree analysis (ETA) will be used to develop (accident) scenario-based
models that imply sequences of system states, safety mechanisms, failures, and
system operator actions. One can get the model assumptions behind the computation of given probability from an event tree (ET) diagram. A generic ET diagram
is presented in Fig. 3.2 and renders:
• The initial event (left-hand-most box);
• The sequence of events (system or circumstantial states, human actions, or
protective systems), if occurring/fail would drive the system—the rest of the top
boxes into a failure state;
• The success and failure branches (solid and dotted lines, respectively) associated
with each state/protective system/action;
• The success and failure terminal points (gray versus black indices).
26
3 Quantitative Probability Assessment of Loc Accident
Fig. 3.2 A generic event tree
We denote the following:
ki as the relative frequency of the initial event occurrence; the index identifies the
current event tree position in the overall computational flow. Its value is purely
supportive being provided for assistance in following the equations and event tree
sequence; having the event trees indexed, however, eases an eventual matrix representation of the computational values;
qij is the <success> probability associated with event j (branch at depth j); qij is the
random variable value of the corresponding chance node; the i index relates to the
associated event tree index;
ð1 pij Þ is the <failure> probability associated with event j.
qk is full pathway k probability.
Pffailurejtriggerg is the probability of failure due to a trigger (an initial event).
The concepts of Markov models and optimization are adopted for the estimation
of reliability and availability of components with a constant failure rate, prone to
continuous wear and tear and subject to routine inspection and repair (when
experiencing a real or an incipient failure) procedures.
Additionally, load-related fatigue models for estimating the failure rates as
related to the cumulative stress exerted on the piece of equipment resulting from the
cumulative load carried or distance travelled (non-constant mean time between
failures (MTBF) components). Defect data analysis based on Weibull distribution
has been adopted in this case.
In this chapter, the rail and road LOC accident frequency computation models
are structurally similar in the sense that both take into account disruptive factors
resulting from the failures of the transportation infrastructure, human errors, and
rolling infrastructure.
The subsequent models and algorithms are based on the literatures (Gheorghe
et al. 2003, 2004, 2005) and have been implemented in a number of software tools
(Gheorghe et al. 2003, 2006).
3.2 Models and Algorithms: Loc Accident Probability …
3.2
27
Models and Algorithms: Loc Accident Probability
in Transportation by Rail
The master logic diagram depicting the mechanism of occurrence of a LOC accident is given in Fig. 3.3. Accordingly, one may notice that the LOC can occur as a
result of two major events: train/tank car collision (COL) and derailment (DER).
A collision is defined as the situation in which the confinement tank physically
interacts with another object resulting in a structural failure of the first.
A derailment is defined as an incident in which the train locomotive or one or more
rail vehicles leave the tracks. Notice that the conditional probabilities of loss of
containment due to tank damage following derailment should be computed with
respect to the type of the tank and the derailment characteristics (freight speed, etc.).
For simplicity, only a priori values, which can be obtained through expert judgment, are considered in the subsequent models.
Fig. 3.3 MLD example for the LOC accident occurrence for rail transportation
28
3 Quantitative Probability Assessment of Loc Accident
In the following section is provided a set of algorithmic descriptions, individual
models, and equations for computing the probability of LOC accident for railroad
transportation.
3.2.1
Computational Scheme for LOC Accident by Rail
1. Probability of loss of containment
PfLOCg ¼ PfLOCjCOLg þ PfLOCjDERg
ð3:1Þ
with
2. Probability of loss of containment due to collision PfLOCjCOLg
PfLOCjCOLg ¼ PfLOCg fReleasejCOLg
ð3:2Þ
and
3. Probability of loss of containment due to derailment PfLOCjDERg
PfLOCjDERg ¼ PfLOCg fReleasejDERg
ð3:3Þ
4. Probability of collision PfCOLg
PfCOLg ¼ PfCOLjFixedObjectsg
þ PfCOLjOtherTraing
þ PfCOLjShuntingg
ð3:4Þ
5. Release probability due to collision, PfReleasejCOLg
PfReleasejCOLg: Obtained from statistics=expert judgment
ð3:5Þ
6. Probability of derailment, PfDERg
PfDERg ¼ PfDERjTracksg
þ PfDERjRollingStockg
ð3:6Þ
þ PfDERjOperationg
7. Release probability due to collision, PfReleasejCOLg
PfReleasejDERg: Obtained from statistics=expert judgment
ð3:7Þ
3.2 Models and Algorithms: Loc Accident Probability …
29
8. Probability of collision with a fixed object, PfCOLjFixedObjectg
PfCOLjFixedObjectg ¼ ft ½Q1 þ Q2 ðx0 Þ þ Q3 ðxi Þ dxxi
ð3:8Þ
with
ft
daily train passage frequency (1/day). Obtained from statistics and/or
expert judgment.
Q1
the probability that an improperly loaded train leaves the station
undetected. Obtained from statistics and/or expert judgment;
Q2 ðx0 Þ the probability that a train initially properly loaded becomes
improperly loaded after x0 kilometers. Obtained from statistics
and/or expert judgment;
Q3 ðxi Þ the probability of a foreign object on tracks will remain undetected at
location xi ;
dxxi
the Kronecker delta, defined by:
dxxi ¼
1
0
for x ¼ xi
for x ¼
6 xi
ð3:9Þ
9. Probability of collision with another train, PfCOLjOtherTraing
PfCOLjOtherTraing ¼ fA ½QS þ QL QTR
ð3:10Þ
with
fA
QS
QL
QTR
frequency of trains on the railway segment in one day (1/day). Obtained
from statistics and/or expert judgment;
the probability of accident due to a switch failure;
the probability of accident due to red-light passing;
the probability of another train on the same track.
Notice that Eq. (3.12) expresses the assumption that collision with another train
may be triggered only by two complementary events: a human fault—the
violation of the red signal by the train operator (driver) and an infrastructure
malfunction—switch failure. Irrespective of the triggering events, the subsequent events that may lead to an actual collision are the same. Figure 3.4
represents an event tree capturing collision with another train. Accordingly, if
human error is involved, the collision could be avoided by train’s protection
systems that detect anomalies. Otherwise, the train protection systems are
irrelevant since there is no ‘fault’ that they could capture.
10. Probability of collision due to switch failure, QS
According to the event tree in Fig. 3.4,
30
3 Quantitative Probability Assessment of Loc Accident
Fig. 3.4 An event tree diagram for the computation of QS and QL . Correlate with Eqs. (3.11)
and (3.12)
QS ¼ q7 þ q8 þ q9
ð3:11Þ
with
q7 ¼ k1 ð1 p15 Þ p14 p13 ð1 p11 Þ
q8 ¼ k1 ð1 p14 Þ p13 ð1 p11 Þ
q9 ¼ k1 ð1 p13 Þ ð1 p11 Þ
and
k1 frequency of switch failure (1/day). Obtained from statistics and/or expert
judgment.
11. Probability of collision due to red-light passing, QL
According to the event tree in Fig. 3.4,
QL ¼ q3 þ q4 þ q5 þ q7 þ q8 þ q9
with
q3 ¼ ð1 k1 Þ p11 ð1 p12 Þ p13 p14 ð1 p15 Þ
q4 ¼ ð1 k1 Þ p11 ð1 p12 Þ p13 ð1 p14 Þ
q5 ¼ ð1 k1 Þ p11 ð1 p12 Þ ð1 p13 Þ
ð3:12Þ
3.2 Models and Algorithms: Loc Accident Probability …
31
and
ð1 k1 Þ frequency of the human error of passing the red signal (1/day)—in the
assumptions stated at 9.
12. Probability of accident when another train is on tracks, QTR
QTR ¼
T0 s
T0
ð3:13Þ
with
T0 the time unit considered when adopting fA (e.g., 1 day);
s total duration the segment is empty, in the same unit as T0 .
To clarify the computation of QTR , let us suppose a track segment of5 km
1
. The
length. The frequency of trains over the segment is five per day fA ¼ 5 day
average speed of a train over the segment is 80 km/h. The corresponding time
required by the train to pass over the segment is 5=80 ¼ 0:625 h 0:0026 day.
Since we have 5 trains each requiring 0.0026 days, we get the total duration the
segment is empty, s ¼ 1 0:0026 ¼ 0:9974; which would lead to a value of
QTR ¼ 0:0026.
13. Probability of collision during shunting, PfCOLjShuntingg
According to the event tree in Fig. 3.5,
PfCOLjShuntingg ¼ q4 þ q5
ð3:14Þ
Fig. 3.5 An event tree diagram for the computation of PfCOLjShuntingg. Correlate with
Eq. (3.14)
32
3 Quantitative Probability Assessment of Loc Accident
with
q4 ¼ k2 ð1 p21 Þ ð1 p22 Þ p23 ð1 p24 Þ
q5 ¼ k2 ð1 p21 Þ ð1 p22 Þ ð1 p23 Þ
and
k2 frequency of car entering track with excess speed (1/day). Obtained from
statistics and/or expert judgment.
14. Probability of derailment due to tracks, PfDERjTracksg
PfDERjTracksg ¼ PfDERjStateOfTracksg
þ PfDERjTonnageg
þ PfDERjTrackIsolationFailureAndTrackClosed g
þ PfDERjTrackIsolationFailureAndTrackOpeng
ð3:15Þ
15. Probability of derailment due to rolling stock, PfDERjRollingStock g
PfDERjRollingStockg ¼ PfDERjBearingsg þ PfDERjBogiesg
ð3:16Þ
16. Probability of derailment due to operational errors, PfDERjOperationalg
PfDERjOperationalg Obtained from statistics=expert judgment
ð3:17Þ
17. Probability of derailment due to tracks’ state, PfDERjTracksg
PfDERjStateOfTracksg over a railway section is computed as a function of the
average unavailability of the respective section and the average frequency of train
passage over the section. This is denoted as follows:
PfDERjStateOfTracksg ¼ 1 eft U
ð3:18Þ
with
the average train passage frequency over the segment (in 1/day);
ft
U the average unavailability of the segment (in day).
Since the expected probability is sufficiently small, one may consider only the
first term of the exponential power series; thus, Equation [3.18] becomes
3.2 Models and Algorithms: Loc Accident Probability …
PfDERjStateOfTracksg ¼ ft U 33
ð3:19Þ
It is also assumed that derailment may only occur during the unavailability of the
segment; hence, the average unavailability U* encompasses the triggering events
that put the system into a derailment-prone state, but also takes into account other
infrastructure failures and human actions that actually lead to derailment. This
entails that U expresses the following mechanisms:
(a) the system (railway) is in an abnormal operational (failure) state when:
–
–
–
–
the track lost its geometry (e.g., parallelism);
the track suffered a structural damage;
there is a switch failure;
there is a foreign object on tracks;
(b) the abnormal states are detected by system’s operators during periodic
inspections;
(c) system operators resolve the problem, thus putting the system back into a
normal operational state.
However, since we are referring to the railway system,
(a) resolving the problem also implies that the track is temporarily out of order
being ‘isolated’ during the repair and
(b) any repair takes time (during which the segment is still unavailable).
The analytical expression of the aforementioned involves:
U ¼ U1 þ U2 þ Q
ð3:20Þ
with
U1 the segment unavailability due to the system in an abnormal state (in 1/day);
the value includes the time duration between inspections and the time duration
required for repair;
U2 the segment unavailability due to preventive maintenance;
Q the probability of human error to leave a track section in a failed state, after the
completion of maintenance.
U1 sums up contributions from each of the failure states; for equation consistency and future identification, we index the system failures as:
1.
2.
3.
4.
Loss of track geometry;
Rail failure (structural damage);
Switch fault;
Foreign object on track.
34
3 Quantitative Probability Assessment of Loc Accident
The equation for U2 is as follows:
U1 ¼
a1
ðT1 þ TR1 Q1 Þ
2
a2
þ ðT2 þ TR2 Q2 Þ
h2a
i
3
þ
ðT3 þ TR3 Q3 Þ þ Q3d
2
a4
þ ðT4 þ TR4 Q4 Þ
2
ð3:21Þ
with
ai
Ti
TRi
Qi
base failure rate for failure type i (1/day);
the time between inspections to detect failure type i (day);
the time required to repair failure type i (day);
the probability of track isolation failure during the repair of failure type
i. These values address human errors that would lead to a track isolation
breach. Each of the values should take into account individual probabilities for:
– Failure of securing and signaling isolation by maintenance personnel;
– Violation of signals or passage conditions by train driver;
– Supervision and checking faults. The individual probabilities mentioned above are not reflected in the equations set for the sake of
simplicity;
Q3d
the probability of an inadvertent switching on demand while train passing
over the switch;
i ¼ 1; 4 failure type identification index above.
One may note that Q3d does not refer to an actual failure of the switch, but rather
to the human error of ‘inadvertent switching.’ However, it has been included under
the switch failure term in Eq. (3.21) for convenience.
U2 in Eq. (3.21) is given by
U2 ¼ fm Tm Q5
ð3:22Þ
with
fm the frequency of preventive maintenance actions (1/day);
Tm average duration of preventive maintenance action (day);
Q5 total probability of track isolation failure, given by
Q5 ¼
4
X
i¼1
Qi
ð3:23Þ
3.2 Models and Algorithms: Loc Accident Probability …
35
The last term of Eq. (2.22), U is
U Obtained from statistics and=or expert judgment
ð3:24Þ
Values ai ; Ti ; TRi ; Qi ; Q3d ; fm ; Tm ; and Q are all model inputs and are given
from statistics and/or expert judgment. Substituting U1 ; U2 and Q in Eq. (3.21) one
gets the extended equation for the probability of derailment due to the state of tracks
as follows:
PfDERjStateOfTracksg ¼ ft na
1
ðT1 þ TR1 Q1 Þ
ha
i
a2
3
þ ðT2 þ TR2 Q2 Þ þ
ðT3 þ TR3 Q3 Þ þ Q3d
2
2
o
a4
þ ðT4 þ TR4 Q4 Þ þ fm Tm Q5 þ U 2
ð3:25Þ
2
Equation (3.25) allows a solid estimation of the probability of derailment due to
the state of the tracks in a ‘traditional’ RAMS philosophy. However, there is an
immediate refinement of the model (Gheorghe et al. 2000b) that allows a better
setup to reflect infrastructure state and other circumstantial and environmental
factors: The analytical expression of this is adjusting (multiplying) the system
failure rates ðasÞ with aggravating factors ðcÞ. Let us consider cenv the set of
environment-related aggravating factors; the environment refers to the track segment location characteristics that may influence system failure types 1 (track
geometry) and 2 (structural damage). Table 3.1 illustrates the cenv aggravating
factors that are taken into account in CARGO software, for illustration.
cswitch is the set of switch types’ aggravating factors; these factors are provided
for taking into account different models of switches that (by design or operational
characteristics) may influence the switch failures (failure type 3). cpo is the set of
aggravating factors depending on the presence and state of protective systems
against foreign objects along the segment (Table 3.2) and can influence failure type
4 (foreign objects on tracks), and cvic is the set of aggravating factors depending on
the surrounding area of the segment (plain area versus mountain, etc.), also
influencing failure type 4; the list of the cvic factors in CARGO is also given for
illustration in Table 3.3.
Table 3.1 Environment-related aggravating factors in CARGO
cenv
Environment description
1.0
1.5
1.5
3.0
Normal
Corrosive
Segment characterized by heavy traffic
Segment vulnerable to heavy downpour or snowfall
36
3 Quantitative Probability Assessment of Loc Accident
Table 3.2 Aggravating
factors in CARGO for
protective systems against
foreign objects
cpo
Protective systems state
1.0
2.0
3.0
Fully operational
Deficient
Absent
Table 3.3 Foreign objects’
vulnerability aggravating
factors in CARGO
cvic
Vicinity type
3.0
3.0
2.0
1.0
1.0
1.0
1.0
1.0
1.0
3.0
3.0
1.0
2.0
3.0
2.0
2.0
1.0
3.0
3.0
2.0
1.0
2.0
1.0
1.0
Forest (enclosed)
Forest type 2
Bushland
Groves
Vineyards
Orchards
Gardens
Meadows and arable
Farm pastures
Highland pastures
Alpine land
Lakes
Rivers
Unproductive land
Barren land
Dwelling areas
Dwelling developments
Industrial buildings
Industrial enterprises
Special destination areas
Recreational areas
Street areas
Railway areas/facilities
Airfields
Considering aggravating factors in Eq. (3.25), one gets:
PfDERjStateOfTracksg ¼ ft
n ha
i
a2
1
cenv
ðT1 þ TR1 Q1 Þ þ ðT2 þ TR2 Q2 Þ
2 i
h2a
3
þ cswitch
ðT3 þ TR3 Q3 Þ þ Q3d
2
a4
þ cpo ðT4 þ TR4 Q4 Þ
2
þ fm Tm Q5 þ U g
ð3:26Þ
3.2 Models and Algorithms: Loc Accident Probability …
37
18. Probability of derailment due to tracks, tonnage dependent, is denoted by:
PfDERjTonnageDependentg
The model proposed assumes that derailment occurs when there is a rupture-type
failure of the tracks due to the wear and tear caused by the cumulative weight
traveling over the segment.
Sa
PfDERjTonnageDependentg ¼ 1 e b
ð3:27Þ
with
S
tonnage (million tons) traffic over the rail segment;
a,b empirical constants depending on the track deterioration mechanisms.
19. Probability of derailment due to tracks, isolation failure, and track closed to
traffic is denoted by:
PfDERjTrackIsolationFailure SegmentClosedg
According to the event tree in Fig. 3.6,
Fig. 3.6 An event tree for the computation of PfDERjTrackIsolationFailure SegmentClosedg.
Correlate with Eq. (3.28)
38
3 Quantitative Probability Assessment of Loc Accident
PfDERjTrackIsolationFailure SegmentClosed g
¼ q3 þ q6 þ q8 þ q9 þ q12 þ q15 þ q17 þ q18
ð3:28Þ
with
q3 ¼ k3 ð1 p37 Þ p34 ð1 p33 Þ p32 p31
q6 ¼ k3 ð1 p38 Þ ð1 p37 Þ p35 ð1 p34 Þ ð1 p33 Þ p32 p31
q8 ¼ k3 ð1 p39 Þ p36 ð1 p35 Þ ð1 p34 Þ ð1 p33 Þ p32 p31
q9 ¼ k3 ð1 p36 Þ ð1 p35 Þ ð1 p34 Þ ð1 p33 Þ p32 p31
q12 ¼ k3 ð1 p37 Þ p34 ð1 p33 Þ ð1 p32 Þ p31
q15 ¼ k3 ð1 p38 Þ ð1 p37 Þ p35
ð1 p34 Þ ð1 p33 Þ ð1 p32 Þ p31
q17 ¼ k3 ð1 p39 Þ p36 ð1 p35 Þ ð1 p34 Þ
ð1 p33 Þ ð1 p32 Þ p31
q18 ¼ ð1 p36 Þ ð1 p35 Þ ð1 p34 Þ ð1 p33 Þ ð1 p32 Þ p31
and
k3 frequency of track isolation failure and track closed (1/day). Obtained from
statistics and/or expert judgment.
20. Probability of derailment due to tracks, isolation failure, and track open to
traffic PfDERjTrackIsolationFailure SegmentOpeng
According to the event tree in Fig. 3.7,
PfDERjTrackIsolationFailure SegmentOpeng ¼ q3 þ q4 þ q5 þ q6
ð3:29Þ
Fig. 3.7 An event tree for the computation of PfDERjTrackIsolationFailure SegmentOpeng.
Correlate with Eq. (3.29)
3.2 Models and Algorithms: Loc Accident Probability …
39
with
q3 ¼ k4 p41 p42 ð1 p43 Þ p44 ð1 p45 Þ
q4 ¼ k4 p41 p42 ð1 p43 Þ ð1 p44 Þ
q5 ¼ k4 p41 ð1 p42 Þ
q6 ¼ k4 ð1 p41 Þ
and
k4 frequency of track isolation failure and track open to traffic (1/day).
Obtained from statistics and/or expert judgment.
21. Probability of derailment due to rolling stock and bearings
PfDERjRollingStock Bearingsg
Due to structural damages and/or effects of wear and tear, the box holding the
bearings of a railway truck may lose its packing (usually oil), thus allowing the
excessive overheating of the bearings. This, in turn, may cause a fire or an axle
fracture. When such an overheating of the bearings occurs, the term ‘hot box’
(HB) is used for defining the situation.
To avoid hot box situation, the packing and bearing have to be regularly
inspected on older railway systems. This job was done by humans. It is performed
both in stations (by track-side workers) and during the train run by the train crew
(by looking for sparks or smoke) (Gheorghe et al. 2000a). When a hot spot was
detected, the train was either slowed down (to reduce friction) or stopped to ‘oil the
wheels’—adding packing to ensure the lubrication characteristics.
In recent times, derailments due to overheating of bearings are much rare. This is
attributed to the following: First, on the one hand, there has been a drastic
improvement in bearings technology. For example, the use of ball, roller, or tapered
as opposed to the ‘traditional’ plain bearings drastically reduce the likelihood of
overheating and second the rolling of infrastructure (i.e., automatic hot box
detection (HBD) systems) which have installed along the railways since 1940s.
Even though the HBDs also evolved from the technological standpoint, their role
remained the same over time: Basically, an HBD detects a HB situation and triggers
the alarm (via wired or the most modern wireless links) to stations, offices, or
interlocking towers. Figure 3.8 tries to reflect all the processes above in the computation of the probability of derailment due to bearings overheating.
According to the event tree in Fig. 3.8, one gets
PfDERjRollingStock Bearingsg ¼ q2 þ q3 þ q5 þ q6 þ q7 þ q8
þ q10 þ q11 þ q12 þ q13 þ q14 þ q15 þ q16
ð3:30Þ
40
3 Quantitative Probability Assessment of Loc Accident
Fig. 3.8 An even tree for the computation of PfDERjRollingStock Bearingsg. Correlate with
Eq. (3.30)
with
q2 ¼ k5 p51 p58 ð1 p59 Þ
q3 ¼ k5 p51 ð1 p58 Þ
q5 ¼ k5 ð1 p51 Þ p52 1 p053 p0053 p56 p57 p58 ð1 p59 Þ
q6 ¼ k5 ð1 p51 Þ p52 1 p053 p0053 p56 p57 ð1 p58 Þ
q7 ¼ k5 ð1 p51 Þ p52 1 p053 p0053 p56 ð1 p57 Þ
q8 ¼ k5 ð1 p51 Þ p52 1 p053 p0053 ð1 p56 Þ
q10 ¼ k5 ð1 p51 Þ p52 p053 p54 p55 p57 p58 ð1 p59 Þ
q11 ¼ k5 ð1 p51 Þ p52 p053 p54 p55 p57 ð1 p58 Þ
q12 ¼ k5 ð1 p51 Þ p52 p053 p54 p55 ð1 p57 Þ
q13 ¼ k5 ð1 p51 Þ p52 p053 p54 ð1 p55 Þ
q14 ¼ k5 ð1 p51 Þ p52 p053 ð1 p54 Þ
q15 ¼ k5 ð1 p51 Þ p52 p053
q16 ¼ k5 ð1 p51 Þ ð1 p52 Þ
and
k5 average frequency of hot wheels or bearings overheating (1/day)—from
statistics and/or expert judgment.
and also
p053 the probability of a HBD failure, given by
3.2 Models and Algorithms: Loc Accident Probability …
p053 ¼
kFR Tbi
2
41
ð3:31Þ
with
kFR the average HBD failure rate (1/day);
Tbi time between inspections for HBD failure;
p0053 the probability that a HBD is unavailable due to being repaired, given by
p0053 ¼
kFR TRbi
2
ð3:32Þ
with
TRbi is the average repair time for HBD.
22. Probability of derailment due to rolling stock and bogies,
PfDERjRollingStock Bogieg
PfDERjRollingStock Bogieg: Obtained from statistics=expert judgment
ð3:33Þ
3.3
Models and Algorithms: Loc Accident Probability
in Transportation By Road
This chapter covers the method and quantitative models proposed for probability of
LOC computation in the case of road transportation. We adopt the same posture as
in the case of rail transportation with respect to model assumptions, modeling, and
the analytical tools that help in grasping the phenomenology of such events.
Naturally, the models employed differ since there are differences in mechanisms
involved in producing LOC events in road and rail transportation systems.
3.3.1
Deductively Model the Reality—MLD Development
for LOC During Road Transportation
Let us introduce the MLD that supports the probability computation model for LOC
accidents by road in a step-by-step manner following the deductive modeling
principles.
The first question one must answer when considering LOC accident is ‘when
LOC may happen?’ Well, LOC may follow two major disruptive events: collision
42
3 Quantitative Probability Assessment of Loc Accident
and overturning of the transportation vector (e.g., a lorry). Collision encompasses
the circumstances when a lorry hits an object without overturning. Then, overturning (naturally) covers the cases when a lorry partially or totally overturns.
Consequently, both collision and overturning may result in structural damage of the
container (e.g., a tank) carrying hazardous materials, thus resulting in LOC and
release. Therefore, there is need to provide conditional probabilities of loss of
containment for each of the accident types.
Moving down on the logical pathway, the next questions are ‘what a lorry can
collide with?’ and ‘what makes a lorry to overturn?’ Well, a lorry may collide either
with another (moving) vehicle or with a fixed object. In the case of overturning,
overturning may be triggered by road, lorry-related failures, and the driver himself.
A collision with another vehicle usually implies actions from two or more traffic
participants and may occur:
• Due to violation of traffic rules (usually at crossing areas) by one of the drivers;
• Due to absentmindedness (sudden braking followed by a back hit) of one or
both drivers;
• Due to overtaking.
Several accident scenarios can be developed when considering vehicle collision
at crossing. These scenarios are introduced in the analytical model description by
appropriate inductive models. Overtaking is one of the major causes of accident.
But do all the accidents due to overtaking have the same relevance when considering the loss of containment? Arguably no. This is especially the case when one
considers the differences in a lateral collision during overtaking and a head-on
collision. This differentiation must also be reflected in the MLD.
Furthermore, a collision with fixed objects is an issue. Questions that one might
consider involves: When can this happen? Where are the fixed objects located?
Here is another major difference between rail and road transportation: A lorry going
off the road is as natural as a train following the predefined path of the tracks;
consequently, we should consider and assess both situations, when the lorry hits a
foreign object on/near the road and when the lorry hits a foreign object off the road.
It has been stated that overturning might be caused by the road being in a
dysfunctional state. Moreover, the dysfunctional state of the road can also be
attributed to either the state of the road (quality) or during maintenance procedures
taking place on road. Overturning can also occur when there is a failure of the lorry.
We only consider three distinct classes of failures as relevant: flat tire, mechanical
(other than brakes), and brakes’ failures. This classification was performed after
considering the most frequent lorry-related causes that lead to overturning.
The proposed model also considers ‘which are the driver’s operational faults that
lead to overturning.’ Three cases were appealing after contemplating the most
common causes of overturning: overspeeding, heath (including fatigue), and
environmental factors. The environmental aspect of faults refers to driving miss
conduct when dealing with different environmental factors such as rain, sharp
curves, and mountain road on the road segment. Figure 3.9 shows a master logic
3.3 Models and Algorithms: Loc Accident Probability …
43
Fig. 3.9 An MLD depicting LOC for a road transportation system
diagram depicting the mechanisms for occurrence of an LOC accident and the
identification of initial events.
Up to this point, everything was in place for actual computation of LOC
probability for road transportation. The following section addresses the necessary
analytical models, algorithms, and equations.
3.3.2
Computational Scheme for LOC Accident by Road
1. Probability of loss of containment
PfLOC g ¼ PfLOCjCOLg þ PfLOCjOVERTg
ð3:34Þ
with
2. Probability of loss of containment due to collision, PfLOCjCOLg
PfLOCjCOLg ¼ PfCOLg PfReleasejCOLg
ð3:35Þ
44
3 Quantitative Probability Assessment of Loc Accident
and
3. Probability of loss of containment due to overturning, PfLOCjOVERT g
PfLOCjOVERT g ¼ PfOVERT g PfReleasejOVERTg
ð3:36Þ
4. Probability of collision, PfCOLg
PfCOLg ¼ PfCOLjFixedObjectg þ PfCOLjOtherLorryg
ð3:37Þ
5. Probability of release due to collision, PfReleasejCOLg
PfReleasejCOLg: Obtained from statistics=expert judgment
ð3:38Þ
6. Probability of overturning, PfOVERT g
PfOVERT g ¼ PfOVERTjRoadwayg
þ PfOVERTjLorryg
þ PfOVERTjDrivingg
ð3:39Þ
7. Probability of release due to overturning, PfReleasejOVERT g
PfReleasejOVERT g: Obtained from statistics=expert judgment
ð3:40Þ
8. Probability of collision with a fixed object, PfCOLjFixedObjectg
PfCOLjFixedObjectg ¼ PfCOLjFixedObjectOnStreetg
þ PfCOLjFixelObjectOffStreetg
ð3:41Þ
9. Probability of collision with an object on street, PfCOLjFixedObjectOnStreetg,
which includes the objects near the street (e.g., traffic signs)
PfCOLjFixedObjectOnStreetg ¼ fl ½Q1 þ Q2 ðx0 ; x00 Þ þ Q3 dx0 xi
ð3:42Þ
with
fl
lorry passage frequency (1/day)—obtained from statistics and/or
expert judgment;
Q1
the probability that the lorry, improperly loaded, leaves undetected—
obtained from statistics and/or expert judgment;
Q2 ðx0 Þ the probability that the lorry, initially properly loaded, becomes
improperly loaded after x0 kilometers—obtained from statistics and/or
expert judgment;
Q3 ðxi Þ the probability of a foreign object on road to remain undetected at
location xi ;
dxxi
the Kronecker delta, defined as in Eq. (3.9).
3.3 Models and Algorithms: Loc Accident Probability …
45
10. Probability of collision with a fixed object, off-street, PfCOLjFixed
ObjectOffStreetg.
Two methods of computation are suggested as follows:
10:1 The probability of collision with a fixed object, off-road, may be given by
statistics and/or expert judgment. This approach is most straightforward,
even though it might not be the most appropriate way to include the circumstantial and spatial characteristics of the road segment that influence the
chance of collision with an object off-street. In other words, it is not the same
thing—from PfCOLjFixedObjectOffStreetg perspective. Consider a case of
road transportation along an agricultural area or a forest area as compared to
an urban area. There are chances of having foreign objects off-road, drastically from one case to another. In order to consider the location characteristics, one has to compute PfCOLjFixedObjectOffStreetg as
10:2 a function of land-use type (along the given segment) and the relevance of
various land-use types to addressing the chance of having fixed objects
off-street. This is done through
PfCOLjFixedObjectOffStreetg ¼ q N
X
m i ni
ð3:43Þ
i¼1
with
q
mi
ni
the base rate of probability of collision with objects off-street, given by
statistics and/or expert judgment;
the share of land-use type i along the analyzed segment (kilometers along
land-use i by segment length);
the relevance weight associated with land-use i.
It is recommended to have ni within (0.1, 10) interval (Gheorghe et al. 2000b)
11. Probability of collision with another vehicle (AV), PfCOLjAV g
PfCOLjALg ¼ P COLjAVcrossing
þ PfCOLjAVahead g
þ P COLjAVinitiatingOvertaking
þ P COLjAVduringOvertaking
ð3:44Þ
with
12. Probability of collision with another vehicle at crossing P COLjAVcrossing
According to the event tree in Fig. 3.10,
46
3 Quantitative Probability Assessment of Loc Accident
Fig. 3.10 An event tree for the computation of P COLjAV crossing . Correlate with Eq. (3.45)
P COLjAVcrossing ¼ q3 þ q6
ð3:45Þ
with
q3 ¼ k1 p11 ð1 p12 Þ ð1 p13 Þ
q6 ¼ k1 ð1 p11 Þ ð1 p12 Þ ð1 p13 Þ
and
k1 probability of two cars simultaneously entering the crossing (1/day).
Obtained from statistics and/or expert judgment.
13. Probability of collision with the vehicle ahead PfCOLjAVahead g
According to the event tree in Fig. 3.11,
PfCOLjAVahead g ¼ q2 þ q3
with
q2 ¼ k2 p21 ð1 p22 Þ
q2 ¼ k2 ð1 p12 Þ
Fig. 3.11 An event tree for
the computation of
PfCOLjAV ahead g. Correlate
with Eq. (3.46)
ð3:46Þ
3.3 Models and Algorithms: Loc Accident Probability …
47
Fig. 3.12 An event tree for the computation of P COLjAV initiatingOvertaking . Correlate with
Eq. (3.47)
and
k1 probability of two cars simultaneously entering the crossing (1/day).
Obtained from statistics and/or expert judgment. 14. Probability of head-on collision when overtaking P COLjAVinitiating Overtaking
According to the event tree in Fig. 3.12,
P COLjAVinitiating Overtaking ¼ q3
ð3:47Þ
with
q3 ¼ k3 p31 ð1 p32 Þ ð1 p13 Þ
and
k3 probability that the lorry driver starts the overtaking maneuver—from
statistics and/or expert judgment.
15. Probability of lateral collision when overtaking P COLjAVduringOvertaking
According to the event tree in Fig. 3.13,
P COLjAVinitiatingOvertaking ¼ q2
Fig. 3.13 An event tree for
the
computation of
P COLjAV duringOvertaking .
Correlate with Eq. (3.48)
ð3:48Þ
48
3 Quantitative Probability Assessment of Loc Accident
with
q2 ¼ k4 ð1 p41 Þ ð1 p42 Þ
and
k4 probability that the lorry driver starts the overtaking maneuver—from
statistics and/or expert judgment.
16. Probability of overturning due to roadway PfOVERTjRoadwayg
PfOVERTjRoadwayg ¼ PfOVERTjStateOfRoad g
þ PfOVERTjRoadUnderMaintenanceg
ð3:49Þ
17. Probability of derailment due to state of the road, PfOVERTjStateOfRoad g
We shall adopt a methodology for the estimation of PfDERjStateOfRoad g
similar to the rail transportation case. Hence,
PfDERjStateOfRoad g ¼ 1 efl U
ð3:50Þ
with
fl
the average lorries’ passage frequency over the segment (in 1/day);
U the average unavailability of the segment (in day).
Equation (3.50) can be rewritten as:
PfDERjStateOfRoad g ¼ fl U ð3:51Þ
The model assumes that overturning may only occur during the unavailability of
the segment; hence, the average unavailability U* encompasses the triggering
events that put the system into an overturning-prone state; other infrastructure
failures and human actions that lead to overturning are also taken into account. This
implies that U expresses the following:
• the system (roadway) is in an abnormal operational (failure) state when:
– there is any type of road deterioration (from potholes to collapsed sections);
– there is a foreign object on roadway.
• the abnormal states are detected by system’s operators during periodic
inspections;
• system operators resolve the problem, thus putting the system back into a
normal operational state;
• resolving the problem also implies that the roadway is temporarily ‘isolated’
during the repair; and also
• any repair takes time (during which the segment is still unavailable).
3.3 Models and Algorithms: Loc Accident Probability …
49
A closer look at assumptions above, one may notice that the LOC may not
necessarily be directly triggered by any of the abnormal states of the system.
However, the abnormal states above lead to a well-known situation in road cargo
transportation: sudden movement for avoiding an obstacle, followed by uncontrollable balance of the cargo and by overturning. The analytical expression of the
aforementioned is as follows:
U ¼ U1 þ U2 þ Q
ð3:52Þ
with
U1 the segment unavailability due to the system in an abnormal state (in 1/day);
the value includes the mean time duration between inspections and the mean
time duration required for repair;
U2 the segment unavailability due to preventive maintenance;
Q the probability of human error to leave the roadway in a failed state, after the
completion of maintenance;
U1 sums up contributions from each of the failure states; system failures are
indexed as follows:
1. Deteriorated roadway;
2. Foreign object on road.
The equation for U1 is as follows:
U1 ¼
a1
a2
ðT1 þ TR1 Q1 Þ þ ðT2 þ TR2 Q2 Þ
2
2
ð3:53Þ
with
ai
Ti
TRi
Qi
base failure rate for failure type i (1/day);
the mean time between inspections to detect failure type i (day);
the mean time required to repair failure type i (day);
the probability of road isolation failure during the repair of failure type
i. These values address human errors that would lead to a road isolation
breach. Each of the values should include individual probabilities for:
– Failure of securing and signaling isolation by maintenance personnel;
– Violation of traffic signs by the driver;
– Supervision and checking faults. The individual probabilities mentioned above are not reflected in the equation set for the sake of
simplicity;
i ¼ 1; 2 failure type identification index.
50
3 Quantitative Probability Assessment of Loc Accident
In Eq. (3.52), U2 is given by
U2 ¼ fm Tm Q3
ð3:54Þ
with
fm the frequency of roadway preventive maintenance actions (1/day);
Tm average duration of preventive maintenance action (day);
Q3 total probability of road isolation failure, given by
Q3 ¼
2
X
Qi
ð3:55Þ
i¼1
The last term of Eq. (3.52), U , is
U is obtained from statistics and=or expert judgment
ð3:56Þ
Values ai ; Ti ; TRi ; Qi ; fm ; Tm ; and Q are all model inputs and are given from
statistics and/or expert judgment. Substituting U1 ; U2 and Q in Eq. (3.19), one gets
the extended equation for probability of derailment due to the state of tracks as
follows:
PfDERjStateOfRoad g ¼ ft þ
na
1
ðT1 þ TR1 Q1 Þ
2
a2
ðT2 þ TR2 Q2 Þ
2
o
ð3:57Þ
þ fm Tm Q5 þ U Similar to the case of rail transportation, there is an immediate refinement of the
model (Gheorghe et al. 2000b) that allows a better setup to reflect infrastructure
state and other circumstantial and environmental factors: The analytical expression
of this is adjusting (multiplying) the system failure rates (a s) with aggravating
factors ðcÞ.
Let us consider cenv , the set of environment-related aggravating factors; the
environment refers to the track segment location characteristics that may influence
system failure types 1 (track geometry) and 2 (structural damage). Table 3.4
illustrates the cenv aggravating factors that are taken into account in CARGO
software, for illustration.
cpo is the set of aggravating factors depending on the presence and state of
protective systems against foreign objects along the road segment and can influence
failure type 2 (foreign objects on tracks). Table 3.5 presents a range of protective
systems states against foreign aggravating factors. cvic is the set of aggravating
factors depending on the surrounding area of the segment such as a plain area as
opposed to a mountainous area, also influencing failure type 2. The list of the cvic
factors in CARGO is given in Table 3.6 for illustration.
3.3 Models and Algorithms: Loc Accident Probability …
51
Table 3.4 Environmentrelated aggravating factors in
CARGO
cenv
Environment description
1.0
1.5
3.0
Normal
Segment characterized by heavy traffic
Segment vulnerability to heavy downpour or snowfall
Table 3.5 Protective systems
states against foreign objects’
aggravating factors in
CARGO
cpo
Protective systems state
1.0
2.0
3.0
Fully operational
Deficient
Absent
Table 3.6 Foreign objects’
vulnerability aggravating
factors in CARGO
cvic
Vicinity type
7.0
6.0
5.0
5.0
1.0
1.0
1.0
3.0
2.0
2.0
3.0
1.0
2.0
3.0
2.0
2.0
1.0
5.0
6.0
2.0
1.0
10.0
1.0
1.0
Forest type 1
Forest type 2
Bushland
Groves
Vineyards
Orchards
Gardens
Meadows and arable
Farm pastures
Highland pastures
Alpine land
Lakes
Rivers
Unproductive land
Barren land
Dwelling areas
Dwelling developments
Industrial buildings
Industrial enterprises
Special destination areas
Recreational areas
Street areas
Railway areas/facilities
Airfields
52
3 Quantitative Probability Assessment of Loc Accident
Notice that even though the types are the same as in the rail transportation case
(see Table 3.3), the values differ since the relevance of each area differs from road
to rail case. Considering the aggravating factors in Eq. (3.57), one gets:
n
a1
cenv þ cpo ðT1 þ TR1 Q1 Þ
2
a2
þ cvic ðT2 þ TR2 Q2 Þ
2
o
PfDERjStateOfRoad g ¼ ft ð3:58Þ
þ fm Tm Q5 þ U 18. Probability of overturning when
PfOVERTjRoadUnderMaintenanceg
road
is
under
maintenance
PfOVERTjRoadUnderMaintenanceg ¼ q3 þ q6 þ q8 þ q9
ð3:59Þ
According to the event tree in Fig. 3.14,
with
q3 ¼ k5 p51 ð1 p52 Þ ð1 p53 Þ
q6 ¼ k5 ð1 p51 Þ p52 ð1 p53 Þ ð1 p54 Þ
q8 ¼ k5 ð1 p51 Þ ð1 p52 Þ p53 ð1 p54 Þ
q9 ¼ k5 ð1 p51 Þ ð1 p52 Þ ð1 p53 Þ
Fig. 3.14 An event tree for the computation of PfOVERTjRoadUnderMaintenanceg. Correlate
with Eq. (3.59)
3.3 Models and Algorithms: Loc Accident Probability …
53
Fig. 3.15 An event tree for
the computation of
PfOVERTjBrakeFailureg.
Correlate with Eq. (3.61)
and
k5 frequency of road under construction or maintenance.
18. Probability of overturning due to lorry PfOVERTjLorryg
PfOVERTjLorryg ¼ PfOVERTjBrakeFailureg
þ PfOVERTjLorryMechanicalFailureg
ð3:60Þ
þ PfOVERTjFlatTireg
with
19. Probability of overturning due to brake failure PfOVERTjBrakeFailureg
According to the event tree in Fig. 3.15,
PfOVERTjBrakeFailureg ¼ q2 þ q3 þ q5 þ q6
ð3:61Þ
with
q2 ¼ k6 p61 p62 ð1 p63 Þ
q3 ¼ k6 p61 ð1 p62 Þ
q5 ¼ k6 ð1 p61 Þ p62 ð1 p63 Þ
q6 ¼ k6 ð1 p61 Þ ð1 p62 Þ
and
k6 relative frequency of brake failures.
20. Probability
of
overturning
due
PfOVERTjLorryMechanicalFailureg
to
mechanical
failure,
54
3 Quantitative Probability Assessment of Loc Accident
Fig. 3.16 An event tree for the computation of PfOVERTjFlatTireg. Correlate with Eq. (3.63)
PfOVERTjLorryMechanicalFailureg: Obtained from statistics=expert judgment
ð3:62Þ
21. Probability of overturning due to flat tire PfOVERTjFlatTireg
According to the event tree in Fig. 3.16,
PfOVERTjFlatTireg ¼ q3 þ q5
ð3:63Þ
with
q3 ¼ k7 ð1 p71 Þ p72 ð1 p73 Þ
q5 ¼ k7 ð1 p71 Þ ð1 p72 Þ ð1 p73 Þ
and
k7 relative frequency of flat tire.
22. Probability of overturning due to driver PfOVERTjDriver g
PfOVERTjDriver g ¼ PfOVERTjOverSpeedingg
þ PfOVERTjDriverStateOfHealthg
ð3:64Þ
þ PfOVERTjTopographyg
with
23. Probability of overturning due to overspeeding, PfOVERTjOverSpeed g
PfOVERTjOverSpeedingg: Obtained from statistics=expert judgment ð3:65Þ
3.3 Models and Algorithms: Loc Accident Probability …
55
24. Probability of overturning due to driver’s state of health, PfOVERTjDriver
StateOfHealthg
PfOVERTjDriverStateOfHealthg: Obtained from statistics=expert judgment
ð3:66Þ
25. Probability of overturning due to topography, PfOVERTjTopographyg
PfOVERTjTopographyg: Obtained from statistics=expert judgment ð3:67Þ
References
Gheorghe, A. V., Grote, G., Kogelschatz, D., Fenner, K., Harder, A., Moresi, E. et al. (2000a).
Integrated risk assessment, transportation of dangerous goods: Case study. Zurich,
Switzerland: Target: Basel-Zurich/VCL. ETH KOVERS.
Gheorghe, A. V., Vamanu, D. V., & Vamanu, B. I. (2000b). SBW: Risk in the transportation of
hazardous materials by road [Computer software]. ETH Zurich: Laboratorium fur Siecherheist
Analytik (LSA) KOVERS-KT
Gheorghe, A. V., Birchmeier, J., Kröger, W., & Vamanu, D. V. (2003). Hot spot based risk
assessment for transportation dangerous goods by railway: Implementation within a software
platform. In Proceedings of the Third International Safety and Reliability Conference
(KONBIN 2003). Gdynia, Poland.
Gheorghe, A. V., Birchmeier, J., Kröger, W., Vamanu, D. V., & Vamanu, B. (2004). Advanced
spatial modelling for risk analysis of transportation dangerous goods. In C. Spitzer, U.
Schmocker & V. N. Dang (Eds.), Probabilistic safety assessment and management (pp. 2499–
2504). London, UK: Springer London. Retrieved from http://link.springer.com/chapter/10.
1007/978-0-85729-410-4_401
Gheorghe, A. V., Birchmeier, J., Vamanu, D., Papazoglou, I., & Kröger, W. (2005).
Comprehensive risk assessment for rail transportation of dangerous goods: A validated
platform for decision support. Reliability Engineering and System Safety, 88(3), 247–272.
http://doi.org/10.1016/j.ress.2004.07.017
Gheorghe, A. V., Masera, M., Weijnen, M. P. C., & De Vries, J. L. (Eds.). (2006). Critical
infrastructures at risk: Securing the European electric power system (Vol. 9). Dordrecht, the
Netherlands: Springer.
Chapter 4
Loc Consequence Assessment
Abstract In this chapter, a set of methods and algorithms for quantitative consequence assessment (i.e., health and environmental impact) of accidental releases of
hazardous substances (i.e., toxic and flammable) are presented. The effects are
analyzed through the biological effects produced by different types of physical
effects (phenomena) that occur during or following a loss of containment
(LOC) event.
Consequence assessment of a loss of containment accident is an important phase
required in a sound risk assessment procedure (Gheorghe et al. 2004). Essentially,
consequence assessment implies the evaluation of the impact (e.g., biological,
ecological, and economical) of a disruptive event on the environment and the
exposed public. In the particular case of hazmat transportation, the focus is on the
impact of the environmental releases of potentially dangerous goods (substances)
resulting after a LOC. Depending on the physical and chemical properties of
substances in a containment, as well as containment (storage) type, the release may
occur in different ways, with various effects on the environment and the public.
Similar to the approach undertaken in Chap. 2, the number of fatalities is taken as
the main impact indicator of a LOC accident. Since the number of fatalities depends,
alongside the properties of the substance, on the spatial characteristics of the
transportation system (i.e., number of people actually exposed), the need to rely on
Geographical Information Systems (GIS) becomes palpable. Appendix B covers the
role of GIS and decision support systems (DSS). This is an essential element of the
analysis since, for example, methane explodes in the same way irrespective of the
presence of people around. This calls for an intermediate impact value that would
quantify the effect of an environment release in an unequivocal way. For these
reasons, percentage of lethality is taken as a preferred measure on the remainder of
the models.
The selection of models came as a response to the natural question: What series
of events lead to a fatality starting with a loss of containment? Arguably, this
depends on several factors. However, the nature of the hazardous substance plays a
major role. This substance/material could ignite, explode, or disperse. In this
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_4
57
58
4 Loc Consequence Assessment
research, the corresponding areas of focus (i.e., phenomena) are fire, explosion, and
atmospheric dispersion. Following these phenomena, the damaging physical effects
are heat radiation for fire, shockwave generation and propagation for explosion, and
toxic substance spreading for dispersion.
The death of an individual exposed to any of the aforementioned physical effects
could occur, respectively, due to:
• first, second- and third-degree burns due to heat radiation;
• wounds due to the shockwave;
• acute intoxication due to immersion in a toxic environment.
One way to link physical effects to the impact indicator (lethality percentage) is
through the use of a probit function. In probability theory and statistics, the probit
function is the quantile function associated with the standard normal distribution,
which is commonly denoted as N(0,1). Current research adopts methods developed
by Nederlandse Organisatie voor Toegepast Natuurwetenschappelijk Onderzoek
(TNO) for the calculation of physical effects and possible damages associated with
dangerous substance (Committee for the Prevention of Disasters 1992; van den
Bosch and Weterings 1996). These methods are consistent current research
objectives. To minimize cross-referencing and enable facilitation of reading and
direct implementation, various definitions and equations of the adopted methods are
repeated several times in this chapter in an algorithmic fashion.
4.1
Physical to Biological Effects’ Relationship
Once the physical effects of the hazmat release are known (these can be analytically
computed starting from the chemical and physical characteristics of the substance
and the release environment, as will be detailed in the following chapters), one
needs a way of linking these results to a more risk-relevant indicator. To clarify,
consider the following example: The physical effect of an open fire event following
a gasoline LOC event is quantified by the means of thermal radiation. However,
one needs more risk-relevant information which is related to: ‘the percentage of
population (people) who will die from first degree burns when exposed to flames for
a duration t.’ This information can be obtained using a probit function. A general
definition of a probit function for a variety of possible effects is (van den Bosch and
Weterings 1996):
Probit ¼ a þ b lnðC n Þ
where
Probit measure of the effect;
C
measure of the cause;
a, b, n coefficients.
ð4:1Þ
4.1 Physical to Biological Effects’ Relationship
59
In consideration of the physical effect, a, b, and n are either substance characteristics (i.e., in the case of acute intoxication) or effect characteristics (i.e., in the
case of fire and explosion effects). The C value in the following models relates to
(i) the thermal radiation, (ii) shockwave pressure, and (iii) the toxic dose. The effect
(E) is the lethality percentage.
The probit function does not provide the actual percentage. In most cases, this
value is typically supplied in the format of a ‘percentage versus probit value’ in
tables. However, one can use an analytical approach to obtain the percentage value
through the use of an error function:
Probit 5
pffiffiffi
Perc ¼ 50 1 þ erf
2
ð4:2Þ
with erfðzÞ—the error function, defined as:
2 Zz 2
erfðzÞ ¼ pffiffiffi et dt
p0
ð4:3Þ
A numerical solution for Eq. (4.3) is given by the polynomial approximation
(Gheorghe and Vamanu 1996):
erfðzÞ ¼ 1 0:254829592 t 0:284496736 t2
þ 1:421413741 t3 1:453152027 t4
2
þ 1:061405249 t5 ex
ð4:4Þ
with
t ¼ 1 þ1p z and p ¼ 0:3275911 for z 0
and
erfðzÞ ¼ erf ðjzjÞ for z\0
4.2
ð4:5Þ
Fire Consequence Assessment
Consequences of fire are quantified by the percentages of exposed population,
located at a given distance (d) from the thermal radiation source, that die due to
first-, second-, and third-degree burns.
When a fire occurs, heat is transferred to the surroundings by the means of
convection and radiation. This suggests using a probit function having parameters
of total heat radiation load (Q) received by a human subject at distance d from the
60
4 Loc Consequence Assessment
source of fire and exposed for a time period texp. In other words, an individual
exposed to Q for a time span texp suffers burns which produce death.
The total heat radiation load is given by:
Q ¼ texp q4=3
ð4:6Þ
with
q
heat radiation load experienced by the receiver per unit area;
texp exposure time.
In the adopted analytical methods, the computation of the heat load work under
the following assumptions (van den Bosch and Weterings 1996):
• Flame is considered to have a finite surface radiator (the visible part of the
flame);
• The flame is characterized by a given radiation emittance (E), in turn;
• E depends on the flame temperature (Tmax);
• Tmax depends on the type of material burning;
• Heat radiation load (q) is proportional to the flame emittance (E) and depends on
the dimensions of the radiator and distance to the radiator; this dependency is
expressed in the form of the view factor (F);
• Heat radiation load at distance d is influenced (reduced) by the atmospheric
transmissivity factor sa .
In consideration of the above, one has the equation for the heat radiation load as:
q ¼ E F sa
ð4:7Þ
Probit coefficients are provided for each of the burn degrees; the equations for
the probit values are:
Probit1 ¼ 39:83 þ 3:0186 lnðQÞ for first degree burns;
Probit2 ¼ 43:14 þ 3:0186 lnðQÞ for second degree burns; and
ð4:8Þ
Probit3 ¼ 36:38 þ 2:5600 lnðQÞ for third degree burns
Once the probit values are known, the lethality percentages can be obtained
using Eq. (4.2). If one adopts a conservative posture (i.e., worst-case scenario
philosophy), then
• air transmissivity is taken as 1 (i.e., sa ¼ 1);
• a subject is exposed to flame’s heat radiation load throughout the lifetime of the
flame (i.e., texp ¼ time while flame exists);
• several constants are used in the model. These constants are presented in
Table 4.1.
4.2 Fire Consequence Assessment
Table 4.1 Constants used in
the computational algorithms
61
List of constants
Symbol
Unit
Value
Gravitational force
Stefan–Boltzmann
G
rB
9.81
5.67E-11
Molar mass air
Mair
Ideal gas constant
Rgas
m/s2
kW
m2 K4
kg
kmol
l Atm
K
Emittance
Atmospheric
transmissivity
e
s
28.9467
0.082
1
1
The models proposed also assume that anyone within the fire radius can be
killed—lethality percentage equals 100 (Gheorghe et al. 2003). The maximum
effect radii are determined in an iterative manner: Lethality percentage due to first-,
second-, and third-degree burns is computed for distances starting from fire radius
with a given measurement step (usually 1 m). The maximum radius for an effect is
given by the distance at which the lethality percentage falls under a given threshold
(e.g., 1 %). Therefore, one needs the caloric load (Eq. 4.6) which entails computing
the thermal radiation level (q) and the exposure time (texp) to compute lethality
percentage.
Three types of fire considered: pool fire, flare, and boiling liquid expanding vapor
explosion (BLEVE). Each of these may follow a LOC accident, depending on the
factors such as the accident mechanics (e.g., puncture of the vessel above the liquid
level), storage type (e.g., pressurized versus unpressurized), and the physical and
chemical characteristics of the substance. To determine the type of fire that should be
considered, the schema presented in Fig. 4.1 is recommended. The computational
algorithms and equation set for each of the fire types are considered below.
4.2.1
Pool Fire Consequence Assessment
A pool fire assessment model is provided for covering the scenarios in which the
hazardous (flammable) materials spill out of the tanker—thus forming a hazmat
pool. This is a situation in which heat transfer from the pool substrate causes the
hazardous material to evaporate and form a cold dense vapor cloud. The presence of
any ignition source in the proximity of the pool (notice that this is a frequently
encountered in case of road or rail accidents) may ignite the vapor cloud spill,
forming a pool fire.
Assessment is a two-phase process. In phase one, the task is to determine the flame
emittance (E), temperature (Tmax), and the combustion time (texp). The second phase,
generally referred to as effects computation, is considered with the computation of heat
radiation load q at distance d, which provides the main consequence indicator (i.e.,
62
4 Loc Consequence Assessment
Fig. 4.1 Types of fire by storage and release characteristics. Adapted from van den Bosch and
Weterings (1996)
lethality percentage). As previously mentioned, heat radiation load depends on the
geometry of the flame. The geometry of a pool fire is assumed as a vertical cylinder or
radius poolrad with height hf. Algorithms for each variable are noted below:
4.2.1.1
Inputs
Case characteristics
Substance characteristics
Substance mass
Pool radius
Molar mass
Boiling temperature
Heat of evaporation
m
poolrad
Mol
tBoil
hv
(kg)
(m)
(kg/kmol)
(°C)
(kJ/kmol)
(continued)
4.2 Fire Consequence Assessment
63
(continued)
Meteorological
4.2.1.2
Specific heat
cv
(kJ/(kmol K))
Combustion heat
Temperature
Atmospheric pressure
hc
tambient
Pambient
(kJ/kg)
(°C)
mm Hg
Risk-Relevant Output
Lethality percentage due to first-, second-, and third-degree burns
Maximum flame temperature
Combustion time
Risk radii for lethality due to first-, second-, and third-degree burns
4.2.1.3
Perci ; i ¼ 1. . .3
Tmax
texp
Computational Steps
1. Compute the absolute temperatures (K) as:
Tboil ¼ tboil þ 273:15
Tambient ¼ tambient þ 273:15
ð4:9Þ
2. Compute the air density given the ambient as:
qair
Mair Pambient
760 Rgas Tambient
ð4:10Þ
3. Compute the heat factor as:
Tfactors ¼
cv ðTboil Tambient Þ;
0;
for Tboil [ Tambient
otherwise
ð4:11Þ
4. Compute the burning rate per unit area (evaporation rate) as:
m00 ¼ 0:001 5. Compute:
hc
hv þ Tfactor
ð4:12Þ
64
4 Loc Consequence Assessment
hf
m00
¼ 42 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
df
qair G dp
0:61
ð4:13Þ
with:
df the fire diameter and df = dp = 2 * poolrad
hf the fire height
dp the pool diameter.
6. Compute the flame emittance from the approximation as:
E ¼ 0:35 m00 hc
1 þ 4 hdff
ð4:14Þ
7. The maximum temperature inside the flame is given by:
Tmax ¼
E
4
þ Tambient
rB
14
ð4:15Þ
8. The combustion time is given by:
texp ¼
4.2.1.4
m
m00 Apool
ð4:16Þ
Effects Computation
A pool fire’s geometry is approximated as a vertical cylinder. The health effects
computation (lethality percentage) depends on the view factor of the flame (i.e.,
view factor of a vertical cylinder). The lethality percentage at distance d from the
radiator is obtained by using the following scheme:
1. Compute the maximum view factor ðFmax Þ for a vertical cylinder for distance
d following the sequence as:
hr ¼
hf
poolrad
ð4:17Þ
Xr ¼
d
poolrad
ð4:18Þ
A ¼ ðXr þ 1Þ2 þ h2r
ð4:19Þ
4.2 Fire Consequence Assessment
65
B ¼ ðXr 1Þ2 þ h2r
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)
(
rffiffiffiffiffiffiffiffiffiffiffiffiffi
1
Xr þ 1 Xr2 1 þ h2r
ðXr 1ÞA
pffiffiffiffiffiffi
atan
Fh ¼
atan
p
Xr 1
ðXr þ 1ÞB
AB
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(
!
1 1
hr
hr ðA 2Xr Þ
ðXr 1ÞA
pffiffiffiffiffiffi atan
atan pffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ
Fv ¼
2
p Xr
ðXr þ 1ÞB
Xr AB
Xr 1
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)
hr
ðXr 1Þ
atan
ðXr þ 1Þ
Xr
Fmax ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Fh2 þ Fv2
ð4:20Þ
ð4:21Þ
ð4:22Þ
ð4:23Þ
2. Compute the heat radiation load as
q ¼ E Fmax
ð4:24Þ
3. Compute the probit function for first-, second-, and third-degree burns as:
4
Probit1 ¼ 39:83 þ 3:0186 ln texpB q3
4
Probit2 ¼ 43:14 þ 3:0186 ln texpB q3
4
Probit3 ¼ 36:38 þ 2:5600 ln texpB q3
ð4:25Þ
4. Compute the lethality percentage due to first-, second-, and third-degree burns
as:
Probiti 5
pffiffiffi
Perci ¼ 50 1 þ erf
2
4.2.2
ð4:26Þ
Flare Fire Consequence Assessment
Flare fire consequence assessment model is provided for handling scenarios in
which there is a puncture in the pressurized container of the hazardous material
66
4 Loc Consequence Assessment
such as gas or liquefied gas. Such an event leads to a forced mix of flammable gas
and air that in case of an ignition would produce a flare fire.
The assessment involves determining the flame emittance (E) and temperature
(Tmax) in a first phase, followed by determining the heat radiation load q at distance
d, hence the main consequence indicator (lethality percentage) in a second phase
(the effects computation phase). Note that, in this case, the combustion time, texp, is
not one of the results of the computation. The processes encountered when gas is
released from a pressurized container are highly complex; there are analytical
models for simulating such an event (see van den Bosch and Weterings 1996), yet
for the sake of simplicity, we consider the combustion time as one of the model
inputs (denoted by texpF). The geometry of a flare is also assumed as a vertical
cylinder. The associated algorithms are presented below:
4.2.2.1
Saturation Pressure Constants
K1 = (22.92 + 21.18 + 21.86 + 21.36 + 21.60 + 21.86 + 26.92 + 21.51)/8
K2 = (2.71 + 1.63 + 2.82 + 2.265 + 2.70 + 2.82 + 4.90 + 2.37)/8
K3 = (0.0289 + 0.0209 + 0.0214 + 0.0174 + 0.0166 + 0.0186 + 0.0168 + 0.0114 +
0.0065)/9
K4 = (0.725 + 0.783 + 0.776 + 0.843 + 0.831 + 0.809 + 0.857 + 0.761 + 0.850)/9
4.2.2.2
Inputs
Case characteristics
Substance characteristics
Meteorological
Hole diameter
Pool radius
Molar mass
Boiling temperature
Heat of evaporation
Specific heat
Combustion heat
Saturated vapor pressure (at 4 °C)
Stoichiometric volume ratio
Temperature
Atmospheric pressure
du
texpB
Mol
tBoil
hv
cv
hc
pv20
jst
tambient
Pambient
(m)
(s)
(kg/kmol)
(°C)
(kJ/kmol)
(kJ/(kmol K))
(kJ/kg)
(mm Hg)
(°C)
(mm Hg)
4.2 Fire Consequence Assessment
4.2.2.3
67
Risk-Relevant Output
Lethality percentage due to first-, second-, and third-degree burns
Maximum flame temperature
Combustion time
Risk radii for lethality due to first-, second-, and third-degree burns
4.2.2.4
Perci ; i ¼ 1. . .3
Tmax
texp
Computational Steps
1. Compute the absolute temperatures (K) as:
Tboil ¼ tboil þ 273:15
Tambient ¼ tambient þ 273:15
ð4:27Þ
2. Compute the air density given the ambient as:
qair
Mair Pambient
760 Rgas Tambient
ð4:28Þ
3. Compute the saturated vapor pressure under the given circumstances as:
1
1
pv
pv ¼ pv20 exp 1000 K2 1:013e5 293:15 Tambient
760
ð4:29Þ
4. Compute the combustion rate (evaporation rate) following the sequence as:
pratio ¼ Mol pv
8314 Tambient
pratio
4
1 K3 pKratio
qa ¼
qu
qair
ð4:30Þ
ð4:31Þ
ð4:32Þ
b1 ¼ 50:5 þ 48:2 qa 9:95 q2a
ð4:33Þ
b2 ¼ 23 þ 41 qa
qa
b1
Kal ¼ 0:32 pffiffiffiffiffi
jst
b1 þ b2
qu
ð4:34Þ
ð4:35Þ
68
4 Loc Consequence Assessment
du
Kal
ð4:36Þ
du
pffiffiffiffiffi
2 Kal b2
ð4:37Þ
hf ¼
df ¼
Since we assume the same geometries for flare and pool fire, we may infer the
burning rate from Eq. (4.13) as:
pffiffiffiffiffiffiffiffiffiffiffiffi hf 0:61
m ¼ qair G df 42 df
1
00
ð4:38Þ
5. Compute the flame emittance as:
E ¼ 0:35 m00 hc
1 þ 4 hdff
ð4:39Þ
6. The maximum temperature of the flame is given by:
Tmax ¼
4.2.2.5
E
4
þ Tambient
rB
1=4
ð4:40Þ
Effects Computation
The effects are computed following the method from Sect. 4.2.1. We duplicate the
equation set for the sake of readability. Thus, to obtain the lethality percentage at
distance d from the fire, one should:
1. Compute the maximum view factor ðFmax Þ for a vertical cylinder for distance
d following the sequence as:
hr ¼
hf
poolrad
ð4:41Þ
Xr ¼
d
poolrad
ð4:42Þ
A ¼ ðXr þ 1Þ2 þ h2r
ð4:43Þ
B ¼ ðXr 1Þ2 þ h2r
ð4:44Þ
4.2 Fire Consequence Assessment
69
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)
(
rffiffiffiffiffiffiffiffiffiffiffiffiffi
1
Xr þ 1 Xr2 1 þ h2r
ðXr 1ÞA
pffiffiffiffiffiffi
atan
Fh ¼
atan
p
Xr 1
ðXr þ 1ÞB
AB
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(
!
1 1
hr
hr ðA 2Xr Þ
ðXr 1ÞA
pffiffiffiffiffiffi atan
atan pffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ
Fv ¼
2
p Xr
ðXr þ 1ÞB
Xr AB
Xr 1
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)
hr
ðXr 1Þ
atan
ðXr þ 1Þ
Xr
Fmax ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Fh2 þ Fv2
ð4:45Þ
ð4:46Þ
ð4:47Þ
2. Compute the heat radiation load as
q ¼ E Fmax
ð4:48Þ
3. Compute the probit function for first-, second-, and third-degree burns as:
4
Probit1 ¼ 39:83 þ 3:0186 ln texpF q3
4
Probit2 ¼ 43:14 þ 3:0186 ln texpF q3
4
Probit3 ¼ 36:38 þ 2:5600 ln texpF q3
ð4:49Þ
4. Compute the lethality percentage due to first-, second-, and third-degree burns
as:
Probiti 5
pffiffiffi
Perci ¼ 50 1 þ erf
2
4.2.3
ð4:50Þ
BLEVE Consequence Assessment
A boiling liquid expanding vapor explosion (BLEVE) consequence assessment
model is provided for handling scenarios in which there is catastrophic rupture
(complete failure) of a pressurized container of the hazardous material (gas or
liquefied gas), followed by ignition of the resulting BLEVE gas cloud. In the
proposed model carries the assumption that the BLEVE fire is approximated to a
fireball.
The assessment entails: determine the flame emittance (E), temperature (Tmax),
fireball radius (R) and the fireball duration (tBLEVE) in a first phase; determine the
70
4 Loc Consequence Assessment
heat radiation load q at distance d, hence the main consequence indicator (lethality
percentage) next (the effects computation phase). The flame geometry is that of a
sphere. The associated algorithms are presented below:
4.2.3.1
Input Data
Case characteristics
Substance characteristics
Substance mass
Molar mass
Boiling temperature
Latent heat, vapors
Specific heat
Combustion heat
Temperature
Atmospheric pressure
Meteorological
4.2.3.2
M
Mol
tBoil
hv
cv
hc
tambient
Pambient
Risk-Relevant Output
Lethality percentage due to first-, second-, and third-degree burns
Maximum flame temperature
Duration of fireball
Risk radii for lethality due to first-, second-, and third-degree burns
4.2.3.3
(kg)
(kg/kmol)
(°C)
(kJ/kmol)
(kJ/(kmol K))
(kJ/kg)
(°C)
(mm Hg)
Perci ; i ¼ 1. . .3
Tmax
TBLEVE
Computational Steps
1. Compute the absolute temperatures (K) as:
Tboil ¼ tboil þ 273:15
Tambient ¼ tambient þ 273:15
ð4:51Þ
2. Compute the air density given the ambient as:
qair
Mair Pambient
760 Rgas Tambient
ð4:52Þ
3. Compute the heat factor as:
Tfactors ¼
cv ðTboil Tambient Þ;
0; otherwise
for Tboil [ Tambient
ð4:53Þ
4.2 Fire Consequence Assessment
71
4. Compute the combustion rate (evaporation rate) as:
m00 ¼ 0:001 hc
hv þ Tfactor
ð4:54Þ
5. Compute hf /df, assuming a pool fire of 1 m diameter as:
hf
¼ hf ¼ 42 df
m00
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
qair G dp
0:61
ð4:55Þ
6. Compute the flame emittance as:
E ¼ 0:35 m00 hc
1 þ 4 hdff
ð4:56Þ
For BLEVE, the value of emittance is doubled in accordance with van den Bosch
and Weterings (1996).
7. The maximum temperature inside the flame is given by:
Tmax ¼
2E
4
þ Tambient
rB
1=4
ð4:57Þ
8. The maximum radius of the fireball is:
RB ¼ 3:24 m0:325
ð4:58Þ
9. The duration of the fireball is given by:
tBLEVE ¼ 0:852 m0:26
4.2.3.4
ð4:59Þ
Effects Computation
The lethality percentage at distance d from the fireball is computed as follows:
1. Compute the maximum view factor at distance d for a sphere:
Fmax ¼
RB
d
2
ð4:60Þ
72
4 Loc Consequence Assessment
2. Compute the heat radiation load
q ¼ E Fmax
ð4:61Þ
3. Compute the probit function for first-, second-, and third-degree burns:
4
Probit1 ¼ 39:83 þ 3:0186 ln texpF q3
4
Probit2 ¼ 43:14 þ 3:0186 ln texpF q3
4
Probit3 ¼ 36:38 þ 2:5600 ln texpF q3
ð4:62Þ
4. Compute the lethality percentage due to first-, second-, and third-degree burns:
Probiti 5
pffiffiffi
Perci ¼ 50 1 þ erf
2
4.3
ð4:63Þ
Explosion Consequence Assessment
Explosion consequences (deaths) are caused by the shockwave propagation. In the
proposed model, the fast variation of pressure caused by the shockwave is converted into mechanical impulse. The impulse is the consequence parameter for the
probit functions used for determining the lethality percentages. The impulse value
corresponding to a given pressure is obtained from empirical pressure–impulse
diagrams (van den Bosch and Weterings 1996).
The output of this model is the effects of the shockwave on (1) the population—
as lethality percentage and (2) the environment—as structural damages on buildings. This model carries the assumption that death is caused by:
•
•
•
•
•
lung injuries—due to the shockwave,
head injuries—due to the shockwave,
body injuries—due to the shockwave,
body injuries—due to fragments, and
head injuries—due to fragments from broken windows.
4.3.1
The Algorithm
4.3.1.1
Constants
The relevant constants and their related values are presented in Table 4.2.
4.3 Explosion Consequence Assessment
Table 4.2 Constants
required by the exploration
assessment model
4.3.1.2
Constant
Symbol
Unit
Value
Gravity
Stefan–Boltzmann constant
G
rB
9.81
5.67E-11
Molar mass air
Mair
Ideal gas constant
Rgas
m/s2
kW
m2 K4
kg
kmol
l Atm
K
Emittance
Atmospheric transmissivity
Kiloton
psi to Pa transformation
e
s
kiloton
psi to Pa
J/kt
psi/Pa
28.9467
0.082
1
1
4.182E9
1.45E-4
Inputs
Case characteristics
Substance characteristics
Meteorological
4.3.1.3
73
Substance mass
Yield fraction
Positive phase duration
Subject (adult, child, etc.)
Subject position
Typical fragment shape
Fragment cross section
Window width
Window height
Window thickness
Glass elasticity module
Glass density
m
Yieldproc
texp
subject
position
fShape
Af
aglass
bglass
dglass
Eglass
qglass
Poisson’s coefficient (glass)
Molar mass
Boiling temperature
Latent heat, vapors
Specific heat
Combustion heat
Mass conversion factor
Temperature
Atmospheric pressure
vPoisson
Mol
tBoil
hv
cv
hc
FTNT
tambient
Pambient
(kg)
(s)
(m2)
(m)
(m)
(m)
(Pa)
(kg/m3)
(kg/kmol)
(°C)
(kJ/kmol)
(kJ/(kmol.K))
(kJ/kg)
(ktonne/kg)
(°C)
(mm Hg)
Computational Steps
1. Select a reference subject for the assessment and get the corresponding subject
mass from Table 4.3
74
4 Loc Consequence Assessment
Table 4.3 Available subject
and their corresponding
average mass
Subject
Mass mbody (kg)
‘Adult man’
‘Adult woman’
‘Child’
‘Baby’
75
55
25
5
2. Compute the generic window dynamic load factor (DLF) following the
sequence:
(a) Compute window’s inertia as:
Inertia ¼ qglass dglass aglass bglass a3glass þ b3glass =6
ð4:64Þ
(b) Compute window’s minimum natural frequency as:
fglass
p
¼ 2
1
a2glass
! sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Eglass Inertia
þ 2
qglass dglass ð1 mPoisson Þ
bglass
1
ð4:65Þ
(c) Compute window’s oscillation period as:
1
fglass
ð4:66Þ
texp
Tglass
ð4:67Þ
Tglass ¼
d) Compute ttoT as:
ttoT ¼
e) Compute the dynamic load factor (DLF) as:
8 ttoT
for ttoT 0:3
>
3
>
>
>
8
1
>
1 þ ðttoT 0:3Þ 15
0:7
for 0:3\ttoT 1:0
>
>
>
>
< 1 þ 8 þ ðttoT 1Þ 4 for 1:0\ttoT 2:0
15
15
DLF ¼
12
1
>
1
þ
þ
ð
ttoT
2
Þ
for 2:0\ttoT 3:0
>
15
15
>
>
>
13
1
>
1 þ 15 þ ðttoT 3Þ 30 for 3:0\ttoT 4:0
>
>
>
:
1 þ 13:5
for ttoT 4
15
3. Compute the static load factor for the window following the algorithm:
(a) Compute the window area as:
ð4:68Þ
4.3 Explosion Consequence Assessment
75
Aglass ¼ aglass bglass
ð4:69Þ
b) Compute critical deflection fraction as:
bglass 1:5
Dtodcr ¼ 6 aglass
ð5:70Þ
(c) Compute the static load at iteration zero:
Pst ¼ 2:0e6 2
dglass
0:7
2
A0:18
glass dglass 0:225 aglass
ð4:71Þ
(d) Compute window’s deflection fraction function of the current thickness:
Dtod ¼ 7:6e15 Pst a3glass bglass
4
dglass
ð4:72Þ
(e) If Dtod\Dtodcr
– compute
g ¼ 1þ
1
ðDtodcr Dtod Þ
9
ð4:73Þ
– update Pst
q ! Pst
– repeat step (d) above.
4. Compute the absolute temperature (K) and the atmospheric pressure in pascal:
pambient 1:013e5
760
ð4:74Þ
Tambient ¼ tambient þ 273:15
ð4:75Þ
Pambient ¼
5. Compute air density:
qair ¼ Mair pambient
760 Rgas Tambient
ð4:76Þ
6. Compute the kiloton expression of the yield fraction:
Yield ¼ yieldproc 1000 hc FTNT
ð4:77Þ
7. Compute the RB1, RB3, RB5, RB10, and RB20 effect radii, as shown in
Table 4.4.
76
4 Loc Consequence Assessment
Table 4.4 Explosion effect radii
Effect
Overpressure
(psi)
X1. Vibrating windows
1
Light injuries due to fragments
X2. Residential buildings
3
collapsed
Frequent serious injuries
Possible deaths
X3. Most of the buildings
5
collapsed
Serious injuries
Frequent deaths
X4. Collapse or serious damage
10
of reinforced concrete buildings
Most of the exposed public killed
X5. Collapse or serious damage 20
of reinforced concrete buildings
Lethality percentage next to
100 %
X6. Extrapolation toward the
P1
explosion center
Total demolition and lethality
area
Description and computational formulae
Radius
(m)
Formula
RB1
RB1 = 1000 * Yield0.33 * 2.20
RB3
RB3 = 1000 * Yield0.33 * 1.00
RB5
RB5 = 1000 * Yield0.33 * 0.71
RB10
RB10 = 1000 * Yield0.33 * 0.45
RB20
RB20 = 1000 * Yield0.33 * 0.28
For computing P1, we adopt the Lagrange interpolation polynomial approach
which is also implemented in Gheorghe et al. (2003). Accordingly, one has:
P1 ¼ y1 Lag1 þ y2 Lag2 þ y3 Lag3 þ y4 Lag4 þ y5 Lag5
with
y1 ¼ 1; X1 ¼ RB1
y2 ¼ 3; X2 ¼ RB3
y3 ¼ 5; X3 ¼ RB5
y4 ¼ 10; X4 ¼ RB10
y5 ¼ 20; X5 ¼ RB20
and
ð4:78Þ
4.3 Explosion Consequence Assessment
77
X¼1
ðX X2 Þ ðX X3 Þ ðX X4 Þ ðX X5 Þ
ðX1 X2 Þ ðX1 X3 Þ ðX1 X4 Þ ðX1 X5 Þ
ðX X3 Þ ðX X4 Þ ðX X5 Þ ðX X1 Þ
¼
ðX2 X3 Þ ðX2 X4 Þ ðX2 X5 Þ ðX2 X1 Þ
ðX X4 Þ ðX X5 Þ ðX X1 Þ ðX X2 Þ
¼
ðX3 X4 Þ ðX3 X5 Þ ðX3 X1 Þ ðX3 X2 Þ
ðX X5 Þ ðX X1 Þ ðX X2 Þ ðX X3 Þ
¼
ðX4 X5 Þ ðX4 X1 Þ ðX4 X2 Þ ðX4 X3 Þ
ðX X1 Þ ðX X2 Þ ðX X3 Þ ðX X4 Þ
¼
ðX5 X1 Þ ðX5 X2 Þ ðX5 X3 Þ ðX5 X4 Þ
Lag1 ¼
Lag2
Lag3
Lag4
Lag5
4.3.1.4
Lethality Percentage Due to Overpressure
Compute the probit function and lethality percentage starting from the center of the
explosion up to RB1 radius, with a given resolution (e.g., 1 m), using the following
the sequence:
1. Compute the overpressure at current distance ðPswðxÞÞ as indicated in
Table 4.5:
Psw
Convert the obtained value in pascal: Psw
psi to psa
2. Adjust the overpressure according to the subject position, as indicated in
Table 4.6:
Table 4.5 Overpressure formulae depending on the distance
Distance X (m)
Overpressure Psw(x) (psi)
X
X
X
X
X
Psw
Psw
Psw
Psw
Psw
<
>
>
>
>
RB20
= RB20 and X < RB10
= RB10 and X < RB5
= RB5 and X < RB3
= RB3 and X <= RB1
=
=
=
=
=
P1 + (X − 1) * (20 − P1)/(RB20 − 1)
20 + (X − RB20) * (10 − 20)/(RB10 − RB20)
10 + (X − RB10) * (5 − 10)/(RB5 − RB10)
5 + (X − RB5) * (3 − 5)/(RB3 − RB5)
3 + (X − RB3) * (1 − 3)/(RB1 − RB3)
Table 4.6 Overpressure adjustment formulae depending on the subject position
Subject position
Overpressure adjustment formula
‘Laid’
‘Standing’
‘Standing, next to a wall’
Ps = Psw
Ps = Psw + 5 * Psw2/(2 * Psw + 14 * Pa)
Ps = (8 * Psw2 + 14 * Psw2)/(Psw + 7 * Pa)
78
4 Loc Consequence Assessment
3. Compute the scaled pressure and impulse as:
Pscaled ¼
Ps
Pa
ð4:79Þ
t
Ps exp
2
ffiffiffiffiffiffiffiffiffiffiffiffiffi
iscaled ¼ pffiffiffiffiffi p
Pa 3 mbody
ð4:80Þ
4. Based on the results above, compute:
– Probit value and lethality percentage due to lung injuries:
4:2
1:3
¼ 5:0 5:74 ln
þ
Pscaled iscaled
ð4:81Þ
ProbitLung 5
pffiffiffi
PercLung ¼ 50 1 þ erf
2
ð4:82Þ
ProbitLung
– Probit value and lethality percentage due to head injuries:
ProbitHead ¼ 5:0 8:49 ln
2:43 103
4:0 108
þ
Pscaled
Pscaled iscaled
PercHead
ProbitHead 5
pffiffiffi
¼ 50 1 þ erf
2
ð4:83Þ
ð4:84Þ
– Probit value and lethality percentage due to body injuries:
7:38 103
1:3 109
þ
ProbitBody ¼ 5:0 2:44 ln
Pscaled
Pscaled iscaled
ProbitBody 5
pffiffiffi
ProcBody ¼ 50 1 þ erf
2
ð4:85Þ
ð4:86Þ
5. From the dynamic and static load factors of a glass sheet, compute:
– Probit value and lethality percentage due to head injuries caused by glass
fragments:
4.3 Explosion Consequence Assessment
79
Ps
ProbitHead Glass ¼ 2:67 þ 5:62 ln DLF Pst
ProbitHead Glass 5
pffiffiffi
ProcHead Glass ¼ 50 1 þ erf
2
4.3.1.5
ð4:87Þ
ð4:88Þ
Lethality Percentage Due to Fragments
1. Select the air friction coefficient of the projectiles (fragments) depending on the
considered shape as indicated in Table 4.7:
2. Compute the lethal speed V0 as:
V0 ¼
Cd Af ql u2l texp
2 mfragment
2
ð4:89Þ
with
7 Pa þ 6 Ps
7 Pa þ Ps
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5
ul ¼ Ps qair ð7 Pa þ Ps Þ
ql ¼ qair
ð4:90Þ
ð4:91Þ
3. Depending on mfragment , one gets the probit value as in Table 4.8:
4. Compute the corresponding lethality percentage as:
ProbitFrag 5
pffiffiffi
ProcFrag ¼ 50 1 þ erf
2
Table 4.7 Average fragment
shape and corresponding
friction coefficients
Shape
Friction coefficient, Cd
‘Cylinder—side’
‘Cylinder—base’
‘Sphere’
‘Disc’
‘Cube—side’
‘Cube—edge’
‘Square box—side’
‘Square box—edge’
1.20
0.82
0.47
1.17
1.05
0.80
1.55
2.05
ð4:92Þ
80
4 Loc Consequence Assessment
Table 4.8 Probit equation
function for fragment mass
mfragment
>4.5
0:1 and 4:5
<0.1
4.4
ProbitFrag
13:9 þ 10:54 lnðV0 Þ
m
V02
17:56 þ 5:30 ln fragment
2
m
V 5:115
29:15 þ 2:10 ln fragment2 0
Acute Intoxication Consequence Assessment
The subsequent methodology allows addressing LOC scenarios related to an environmental release of the (toxic) substances. Once the toxic chemical, henceforth
also named pollutant, leaves the container, it is subject to the atmospheric dispersion (i.e., diffusion and advection) process. Consequently, the pollutant concentration in air may exceed a threshold limit and therefore becomes dangerous for
health and life of a population. However, it can be expected that concentration of a
given pollutant will decrease due to diffusion and that the plume will travel due to
advection. Then, of interest includes (1) how long the concentration exceeds one of
the threshold values and (2) what area is affected by the plume during this time.
The following set of models allows for the quantification of the impact of an
atmospheric release of toxic substances in terms of:
• The impact radius (radii) with respect to a given regulatory concentration in air;
• The total time while a regulatory concentration is exceeded;
• The lethality percentage—our core health impact indicator—due to acute
intoxication as a function of distance;
• The time while a concentration resulting in a given lethality percentage is
exceeded.
These models are adopted from the previous research (Committee for the
Prevention of Disasters 1992; Gheorghe et al. 2000; 2003; van den Bosch and
Weterings 1996), and the following assumptions are applicable:
• The entire quantity of pollutant is released at once (instantaneous release);
• The exposure time for a given effect is taken as the time span while the effect
takes place (the overconservative approach).
In light of the above, there are two tasks one must address: For a given quantity
of pollutant and under given environmental conditions, (1) find a way to get the
maximum distance down to which a reference concentration in air is exceeded and
(2) find a way to determine the distance down to which a target percentage of the
population exposed dies due to acute intoxication. These issues are addressed
below.
4.4 Acute Intoxication Consequence Assessment
81
Table 4.9 Different health-related chemical indicators
Indicator
Description
Immediately dangerous to life or
health (IDLH)
Concentration formally specified by a regulatory value
and defined as the maximum exposure concentration of
a given chemical in the workplace from which one
could escape within 30 min. It is likely to cause death
or immediate or delayed permanent adverse health
effects or prevent escape from such an environment
Concentration of an airborne substance to which an
average person can be repeatedly exposed without
adverse effects. TLV is expressed as time-weighted
average, based on an allowable exposure averaged over
a normal 8-h workday or 40-h workweek
Maximum permissible concentration of a material,
generally expressed in ppm in air, for a defined short
period of time (typically 5 or 15 min, depending upon
the country). This ‘concentration’ is generally a
time-weighted average over the period of exposure.
These values, which may differ from country to
country, are often backed up by regulation and
therefore may be legally enforceable
ERPG-1 is the maximum concentration in air below
which it is believed nearly all individuals could be
exposed for up to one hour without experiencing other
than mild transient adverse health effects or perceiving
a clearly defined objectionable odor
ERPG-2 is the maximum concentration in air below
which it is believed nearly all individuals could be
exposed for up to one hour without experiencing or
developing irreversible or other serious health effects
or symptoms that could impair their abilities to take
protective action
ERPG-3 is the maximum concentration in air below
which it is believed nearly all individuals could be
exposed for up to one hour without experiencing or
developing life-threatening health effects
Threshold limit value (TLV)
Short-term exposure limit (STEL)
The Emergency Response Planning
Guidelines (ERPG-1, 2, 3)
4.4.1
Computing the Risk Radii
The aim is to compute the concentrations of a pollutant in a covered area that
exceed a given threshold and the exposure time (i.e., for how long). For simplicity,
the impact area is assumed as the circular extent of radius that is equal to the
maximum distance downwind where the threshold concentration is exceeded (risk
radius). This suggests that one task becomes finding the value of the risk radius.
82
4 Loc Consequence Assessment
From the toxicity point of view, chemicals can be characterized using different
indicators. In a given situation, such indicators will reflect the concentration (i.e.,
g/m3 or ppm) of substance that might have an adverse effect on exposed population.
Table 4.9 shows toxicity indicators (threshold values) based on a classification by
Oxford University.1
The ‘instantaneous release’ assumption leads to adopting the Gauss puff model
for the atmospheric dispersion process. The concentration at a location in space is
given in the puff model by:
Cðx; y; zÞ ¼
x
m
3
ð2pÞ2 rh rv
e
2 þ y2
2r2
h
" e
ðzH Þ2
2r2v
þe
ðz þ H Þ2
2r2
v
#
ð4:93Þ
with
g
Cðx; y; zÞ m3
x ðm)
y ðm)
z ðm)
m ðg)
rh ; rv ðmÞ
H ðm)
the concentration in air at location ðx; y; zÞ, from source;
the downwind distance from source;
the crosswind distance;
the height;
the mass of substance;
the horizontal and vertical dispersion coefficients;
emission height.
If one considers the puff evolution in time irrespective of wind speed (diffusion),
then one denotes:
CT ðg=m3 Þ the threshold concentration of a chemical (any of the toxicity indicators
above);
CT ½ t Rp ðmÞ, the puff radius at time t is defined as the distance from the puff center to
the point in space where concentration equals CT .
In current efforts, we assume that in a particular case of a LOC accident, the
release takes place at ground level ðH ¼ 0Þ. Moreover, we are looking for concentration values at ground level ðz ¼ 0Þ, and since our objective is to compute the
cloud radius, downwind is set at ðy ¼ 0Þ. Consequently, for a given threshold
concentration and moment in time after release, Eq. (4.93) becomes:
CT ¼
m
3
ð2pÞ2 rh rv
e
CT R½t
p
2rh2
ð4:94Þ
From where the risk radius can be inferred as:
1
More information can be retrieved from Physical and Theoretical Chemistry Laboratory, Oxford
University, UK.
4.4 Acute Intoxication Consequence Assessment
Table 4.10 Doury dispersion
coefficient constants by
stability class and time
Time
Ah
83
Kh
Stability class 1 (strong diffusion)
0
4.05E-1
0.859
2.40E2
1.35E-1
1.130
3.28E3
1.35E-1
1.130
9.70E4
4.63E-1
1.000
5.08E5
6.50E0
0.824
1.30E6
2.00E5
0.500
Stability class 2 (weak diffusion)
0
4.05E-1
0.859
2.40E2
1.35E-1
1.130
3.28E3
1.35E-1
1.130
9.70E4
4.63E-1
1.000
5.08E5
6.50E0
0.824
1.30E6
2.00E5
0.500
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
u
u
m
CT ½t
Rp ¼ rh t 2 ln
3
ð2pÞ2 rh rv
Av
Kv
0.42
1.00
20.00
20.00
20.00
20.00
0.814
0.685
0.500
0.500
0.500
0.500
0.20
0.20
0.20
0.20
0.20
0.20
0.500
0.500
0.500
0.500
0.500
0.500
ð4:95Þ
Naturally, a negative value of the logarithm argument means that under the
scenario assumptions (substance, mass, and time), the threshold limit has not been
exceeded.
Up to this point, we have not referred to the dispersion coefficients (rh and rv ) in
Eq. (4.95). In this research, the Doury dispersion coefficient set (Gheorghe and
Vamanu 1996) is adopted. This is a natural choice since the Doury coefficients are
time dependent which is similar to the present discussion. The expression for the
Doury coefficients is:
rh ðtÞ ¼ ðAk tÞKh
ð4:96Þ
rv ðtÞ ¼ ðAv tÞKv
with
Ak ; Kh ; Av and Kv being the time-dependent constants as shown in Table 4.10 for
each of the diffusion classes considered by the model (i.e., weak and strong
diffusion).
At this point, we have a solution (Eq. 4.95) to determine the time evolution of
the stationary puff with respect to a given threshold concentration. To determine the
risk radius associated with a given threshold limit, however, one has to consider that
the puff also ‘travels’ in time (i.e., one has to include the effects of the wind). In
other words, the risk radius is given by the sum of the puff radius at moment t and
the distance traveled by the puff in time t.
84
4 Loc Consequence Assessment
The following notations are necessary:
u ðm=s) is the average wind speed;
d ½t ðm) is the distance traveled by the puff center at time t;
CT ½t
R ðm) is the risk radius at time t.
The following holds:
d ½t ¼ u t
ð4:97Þ
and
(
CT
R½t ¼
½t
d ½t þ CT Rp
CT
R½t1
½t
if d ½t þ CT Rp \ CT R½t1
otherwise
ð4:98Þ
Equation (4.98) ensures that only the new distances travelled by the puff with a
concentration higher than the threshold limit are taken into account. Additional
information on model for atmospheric dispersion can be found elsewhere (e.g.,
Gheorghe 2005).
The last objective in this phase of the assessment is to find out the exposure time
related to a given concentration threshold. The process of computing the risk radii is
iterative (i.e., time sampled). The maximum exposure time for a given concentration equals the time span between the release and the puff extinction (concentration
below the threshold limit). Let us denote:
CT
texp ðs) as the maximum exposure time associated with concentration CT
Summing up, the results of this phase are the following:
(a) Maximum exposure time—the time while the concentration exceeds the
threshold values;
(b) Plume radius at moments of time (starting from 1 s from release until the
maximum exposure time);
c) The risk radii for the assumed threshold concentrations.
4.4.2
Computing the Lethality Percentage
The second phase targets the assessment of the health impact of the hazmat release,
quantified by the lethality percentage due to acute intoxication. Several remarks are
in line. The lethality percentage is again obtained from the probit functions. In this
case, however, the probit function plays the role of a dose-effect equation. The probit
function for acute intoxication is (Committee for the Prevention of Disasters 1992):
Probit ¼ a þ b lnðDÞ
ð4:99Þ
4.4 Acute Intoxication Consequence Assessment
85
where
D is the chemical dose defined as the time-integrated integral of concentration.
Z
ð4:100Þ
D ¼ C n dt
t
The probit coefficients a, b, and n are substance characteristics.
One may notice the difference between the meaning of the probit coefficients in
case of acute intoxication and the previous cases. In the acute intoxication case, the
probit coefficients are a characteristic of the substance, reflecting the impact of the
toxicity of the substance on the subjects. In previous cases, the coefficients characterize the effect itself (e.g., probit coefficients for lung injuries).
It is important to recall the objectives of this phase. Essentially, we are
looking for:
(a) The lethality percentage—our core health impact indicator—due to acute
intoxication as a function of distance;
(b) The time while a concentration resulting in a given lethality percentage is exceeded.
In order to get this information, we approach the problem from the opposite
direction. In fact, even the heading for this subchapter appears, at first glance,
misleading since we start our method from a given lethality percentage. The
problem statement from this inverse perspective might be restated as:
Given the lethality percentage perc, find a way to determine: 1) the maximum distance
downwind from emission source down to which perc exhibits and 2) the maximum
exposure time while the pollutant concentration would cause perc of the exposed population death due to acute intoxication
In order to respond to these questions, there is a need to assess substance and mass, and
the emission characteristics. The first task is to get the probit value that corresponds to
perc (probitperc ). In other words, one needs to find a way to compute the inverse of the
erf function. For this, we propose the adoption/implementation of a fast-converging
iterative algorithm based on the erf approximation as in Eq. (4.2). The actual algorithm
for the inverse problem (i.e. obtaining probitperc starting from perc) is not provided
here, being left as exercise for the interested reader. As an indication, one may opt for a
numerical approach based on the half-interval (binary) search, using the Eq. (4.2).
Once probitperc is known, Eq. (4.99) can be applied to get:
D¼e
probitperc a
b
¼ TICperc
ð4:101Þ
Equation (4.101) also states the time-integrated concentration (TICperc ) for a
given chemical, corresponding to a lethality percentage perc which is equal to D.
In order to get the instantaneous concentration that would be consistent with
probitperc , we consider the exposure time which is equal to the maximum of the
CT
texp values as previously determined. We denote:
86
4 Loc Consequence Assessment
texp ¼ max
C
T
texp
ð4:102Þ
From Eqs. (4.100)–(4.102), we get the value for the concentration Cperc as:
(
TICperc
texp
Cperc ¼
1
n
0;
;
if TIC [ 0
otherwise
ð4:103Þ
The expression of Cperc in mg=m3 is given from:
Cperc ¼
Cperc
mg to ppm
ð4:104Þ
with
mg to ppm ¼
Rgas Ta 760
Molpambient
ð4:105Þ
Next, one now needs to find out where (i.e., the distance from emission source)
one can find concentration value that equals Cperc . This value is found by observing
the results of a previously performed dispersion assessment using the atmospheric
dispersion model introduced in Sect. 4.4.1. The dispersion assessment is performed
for time duration texp and a recommended time sampling of 0:005 texp (Gheorghe
2005). The following section sums up all of the above in algorithmic fashion that is
ready for implementation.
4.4.3
An Algorithm for Acute Intoxication Assessment
Constants in Table 4.11 are required in the algorithm.
Table 4.11 Acute
intoxication consequence
assessment required constants
Constant
Symbol
Unit
Value
Gravity
Molar mass air
Ideal gas constant
G
Mair
Rgas
m/s2
kg/kmol
lAtm
K
9.81
28.9467
0.082
4.4 Acute Intoxication Consequence Assessment
4.4.3.1
Inputs
Case characteristics
Substance characteristics
Meteorological
4.4.3.2
87
Substance mass
Molar mass
Boiling temperature
IDLH
TLV
STEL
ERPG-1
ERPG-2
ERPG-3
Probit a
Probit b
Probit n
Doury stability class
Wind speed
m
Mol
tBoil
IDLH
TLV
STEL
ERPG1
ERPG2
ERPG3
Aprob
Bprob
Nprob
Kt
u
(kg)
(kg/kmol)
(°C)
(mg/m3)
(mg/m3)
(mg/m3)
(mg/m3)
(mg/m3)
(mg/m3)
(m/s) ground level
Computational Steps
Preliminary phase
1. Compute the absolute temperatures (K) as:
Tambient ¼ tambient þ 273:15
Tboil ¼ tboil þ 273:15
ð4:106Þ
2. Compute the air density given the ambient as:
qair
Mair Pambient
760 Rgas Tambient
ð4:107Þ
88
4 Loc Consequence Assessment
Computation of the risk radii of IDLH, TLV, STEL, and ERPG-1, 2, 3
1. The algorithm is based on an iterative process as:
01. The algorithm is based on an iterative process as:
I. Start with t =1 (seconds)
II. Compute the Doury horizontal and vertical dispersion coefficients (
Equation [4.96] and Table 20.
III. Compute the risk radius by following the sequence:
using
(i)
(ii)
If
then
compute
(Equation 4.95)
compute
(Equation 4.98)
Repeat (II)
Else
End
A closer look at the algorithm above, one notices that it allows for simultaneous
risk radii. However, notice that regardless of the implementation choice, at the end
of this phase, one must select the maximum exposure time and the maximum risk
radius such that:
CT
texp
R½t
¼ max CT texp
Rmax ¼ max
CT
These are essential to provide maximum exposure times and risk radii of each of
the threshold concentrations considered (i.e., IDLH, TLV, STEL, ERPG-1, 2, 3).
4.4 Acute Intoxication Consequence Assessment
89
Intermediate phase
1. Create the reference atmospheric dispersion assessment (required for lethality
radii computation) as:
IV. Select the time sampling interval as
V. Start with t = 1 (seconds)
VI. Compute and keep the records of concentration downwind at moment t by:
Computing the Doury horizontal and vertical dispersion coefficients
using Equation [4.96] and Table 20;
Apply Equation [4.94].
Current time t
Puff displacement (location of the center of the puff)
as in Equation [4.97].
VII.
VIII. Repeat (VI) until
End.
Calculation of lethality percentage radii
IX. Start with perc = 99
X. Compute
that is consistent to perc, following the algorithm in Section 4.1.
(
) corresponding to
XI. Compute the instantaneous concentration
by sequentially applying Equations [4.101], [4.103] and [4.105].
XII. Identify in the results of the Intermediate phase the record closest to
in
terms of concentration2 (the reference record)
XIII. Keep record of the following from the reference record.
Lethality percentage
Concentration
Exposure time as
Lethality radius
XIV.
XV. Repeat (X) until perc=0
End.
References
Committee for the Prevention of Disasters. (1992). Methods for the determination of possible
damage. The Hague, the Netherlands: Sdu Uitgevers, Den Haag.
Gheorghe, A. V. (2005). Integrated risk and vulnerability management assisted by decision
support systems: Relevance and impact on governance (Vol. 8). Dordrecht, The Netherlands:
Springer.
Gheorghe, A. V., & Vamanu, D. V. (1996). Emergency planning knowledge. Zurich, Switzerland:
vdf Hochschulverlag AG an der ETH Zurich.
Gheorghe, A. V., Grote, G., Kogelschatz, D., Fenner, K., Harder, A., Moresi, E., Engel, M.,
Papazoglou., & Vamanu, D. (2000). Integrated risk assessment, transportation of dangerous
goods: Case study. Zurich, Switzerland: Target: Basel-Zurich/VCL. ETH KOVERS.
90
4 Loc Consequence Assessment
Gheorghe, A. V., Birchmeier, J., Kröger, W., & Vamanu, D. V. (2003). Hot spot based risk
assessment for transportation dangerous goods by railway: Implementation within a software
platform. In Proceedings of the third international safety and reliability conference (KONBIN
2003). Gdynia, Poland.
Gheorghe, A. V., Birchmeier, J., Kröger, W., Vamanu, D. V., & Vamanu, B. (2004). Advanced
spatial modelling for risk analysis of transportation dangerous goods. In C. Spitzer, U.
Schmocker & V. N. Dang (Eds.), probabilistic safety assessment and management (pp. 2499–
2504). London, UK: Springer London. Retrieved from http://link.springer.com/chapter/10.
1007/978-0-85729-410-4_401
van den Bosch, C. J., & Weterings, R. A. P. M. (Eds.). (1996). Methods for the calculation of
physical effects: Dues to releases of hazardous material (liquids and gases). CPR 14E, Second
and later editions. The Hague, the Netherlands: TNO—The Netherlands Organization of
Applied Scientific Research.
Chapter 5
The Vulnerability Issue
Abstract This chapter provides a working definition for ‘vulnerability’ in the
context of contemporary research. Different models are then presented in an attempt
to formalize the notion of vulnerability for the purposes of quantitative assessment.
Methodological aspects involving system ‘definition’ and ‘indicators’ for quantitative vulnerability assessment are presented.
Risk assessment is a careful and thorough examination of what could go wrong
with a system, which, in turn, would harm people and the environment (de Weck
et al. 2011; Gheorghe et al. 2014; Gibson et al. 2007). Certainly, risk assessment
serves multiple objectives including estimating the extent of the potential damage,
the likelihood of malfunctioning, assessing whether sufficient precautions have
been taken, or if more actions should be done to minimize risk acceptable levels.
Obviously, the raison d’être for risk assessment has to do with the internal characteristics of the process to be analyzed. This last statement can be addressed in the
context of assessment methodology as indicated in Chaps. 2, 3, and 4. In the
transportation of dangerous goods, risk can be depicted as function of (1) the
probability and the frequency of a disruptive event characteristic to the process
(e.g., LOC accident following a trigger event such as a ‘flat tire’ or ‘collision when
entering the crossing’) and (2) the level of consequences of the abnormal event
which could depend on the physical and chemical features of the transported
substance(s) together with other factors including the type of the confinement of the
substance being transported, and (3) the health impact of the event (i.e., lethality).
Yet another perspective requires attention: the threat–subject relationship. When
one talks of risk, the system itself would be the threat. This is especially the case
when the system affects the environment. Then, a pertinent question can arise: How
about the other way around? In essence, can the environment be a threat to the
system?
Social and economic developments as well as large-scale natural and man-made
events continue to indicate that considering elements of risk (i.e., probability and
consequence) is not sufficient to enhance and make systems more resilient
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_5
91
92
5 The Vulnerability Issue
(Gheorghe and Katina 2014; Tokgoz 2012), especially when we consider the need
to make systems more robust and at the same time being able to limit the potential
negative impact to public. This reality has led a major change of perspective with
respect to industrial, economic, and social system safety analysis where dealing
with complex system requires addressing an array of issues including: capability to
grasp the cross-sector dependencies (Shi and Jaeger 2010), dealing with interdependencies (Katina and Unal 2015; Katina et al. 2014; Rinaldi et al. 2001; Vamanu
and Masera 2006) and, by all means, consider and prevent the intentional factor.
The urge to understand the intricate relationships between various entities in
modern society is reflected in security policies on both sides of the Atlantic. For
example, the US Department of Homeland Security noted that enhancing security
and resiliency of national critical infrastructures requires ‘understanding and
addressing risks from cross-sector dependencies and interdependencies …’
(USDHS 2013 p. 13). In the year, the EU adopted a new approach for the European
Critical Infrastructure Protection with the aim of looking at the ‘effects of those
interdependencies [that] are not limited to single countries … [this is especially the
case since] critical infrastructures have a cross border dimension. In addition to
interdependencies between sectors, there are also many interdependencies within
the same sector but spanning a number of European countries. [such as] The
European high-voltage electricity grid, composed of the interconnected national
high-voltage electricity grids’ (European Commission 2013 p. 2).
Complementary to the more architectural and operational-oriented issues is a
concern for protection against the intentional factor and hence a requirement
strongly reflected in official statements, regulatory documents, and research programs (e.g., see Ashcroft et al. 2002; EHC 1999). Protection against terrorism is a
fundamental aspect in the overall Critical Infrastructure Protection. While some
inherent differences on the definition, meaning, and ways to address different issues
in the domain of critical infrastructures, especially on the two sides of the Atlantic
(Katina and Keating 2015), transport and chemical industry hold a top position in
the list.
Addressing this emerging domain comes with tremendous new challenges. After
all, no model-irrespective of its complexity-could had ever predicted that customer
services of a mobile carrier in Great Britain would have suffered in the aftermath of
the Great Tohoku Earthquake due to: the outsourcing of the services in Asia;
adoption of Voice over Internet Protocol (VoIP) as communication protocol; and
structural damage of several Internet submarine cables. One could argue with good
reason that customer services are not the most representative aspects of critical
infrastructures—and current author will tend to agree. However, this seemingly
simple example illustrates the intricate and complex relationships that exist in the
modern world. Moreover, these realities provide the basis for the need to think
out-of-the-box when dealing with these new challenges. This posture is reflected
more and more in the need for new sciences, accompanied by suitable methods,
tools, and techniques that would handle challenges that we currently face and those
that lie ahead.
5 The Vulnerability Issue
93
Moreover, on the understanding that the society cannot pay the costs of total
protection from an economic while still abiding by the democratic principles and
moral balances, identifying and prioritizing complex systems on the basis of vulnerability becomes a must for the new and emerging sciences (Apostolakis and
Lemon 2005; Katina and Hester 2013). However, a question still stands: What is
the vulnerability of a system? Or, stated differently: What makes a system vulnerable? The answer to this seemingly simple question is surprisingly hard to
ascertain. There is a (sad) joke among researchers that says that ‘if you have 10
practitioners in one room, you will receive 15 different responses to the question of
vulnerability.’
A natural consequence of this dynamics is the need for continuous efforts in the
academic—as well as the sociopolitical environments—for the conceptualization,
formalizing, and quantifying the notion of vulnerability. The following section
introduces our approach to this issue as well as its supportive academic posture.
5.1
Definitions and Conceptualization
No one accepted the definition of vulnerability. In fact, the context of the definition
of notion of vulnerability appears to be driven by issues of technical, economic,
social, and political security policies. This confirms the diagnosis on the current
understanding that a fuzzy concept is still in need of operational quantitative
expressions. Crichton (1999) provides one of the most interesting definitions since
it involves risk and vulnerability: ‘Risk’ is the probability of a loss and depends on
three elements: hazard, vulnerability, and exposure.’ This definition lexically
introduces vulnerability as susceptibility of a system to ‘losses’ when ‘exposed’ to
internal or external stress. In fact, a closer look of this definition suggests a cybernetic model, in as much as it involves the concepts of inputs, outputs, and black
box for vulnerability. Figure 5.1 is drawn to represent the cybernetic model for the
notion of vulnerability (Vamanu et al. 2006).
Another class of models emerging from the vulnerability definitions in literature
reflects a sociologic model. Mainly preferred by Scandinavian authors (e.g.,
Stockholm Environment Institute: http://www.sei-international.org/), this model
relies on a triplet of classes: The sociological definition keeps ‘exposure’ as the
main category of vulnerability, yet—by virtue of the sociology mission, places the
human subjects as exposure targets at the end of the logical chain, and at the front
end, the model adds threats (hazards) in the logical chain. Figure 5.2 is drawn to
represent the sociological model for vulnerability (Vamanu et al. 2006).
A third perspective is offered through the semantic model that proposes a tripartite relationship for defining system vulnerability (Jantsch 2005). Accordingly,
vulnerability is seen as part of a relationship between threats, losses, and vulnerability. This relationship is captured in Fig. 5.3.
94
5 The Vulnerability Issue
Fig. 5.1 A cybernetic model for the notion of vulnerability
Fig. 5.2 A sociologic model for vulnerability
Fig. 5.3 A semantic model of
vulnerability
The vulnerability models presented, while not exhaustive, provide insights into
efforts to formalize the concept of vulnerability. In fact, current authors see these
models as complementary as opposed to being contradictory. Supporting this
perspective is the response to the question ‘What/who is the system in connection
with the threat–exposure–subject relationship?’ Our response is ‘the system is the
whole’ including:
• the physical ways and means for framing motivation for threat;
• the exposure channels; and
• the exposure subject(s)—which according to the current understanding includes
environment; critical infrastructures, and last but not least humans.
5.1 Definitions and Conceptualization
95
Lexicographic definitions of risk and vulnerability based on WordNet 1.7
Risk
Vulnerability
Risk
Vulnerability
n 1: a source of danger; ‘drinking alcohol is a health hazard’ [syn: hazard,
jeopardy, peril]
2: a venture undertaken without regard to possible loss or injury; ‘he saw the
rewards but not the risks of crime’; ‘there was a danger he would do the
wrong thing’ [syn: peril, danger]
v 1: expose to a chance of loss or damage; ‘we risked losing a lot of money în
this venture’; ‘why risk your life?’ [syn: put on the line, lay on the line]
2: take a risk in the hope of a favorable outcome; ‘when you buy these stocks
you are gambling’ [syn: gamble, chance, hazard, take chances, adventure,
run a risk, take]
n 1: the state of being vulnerable or exposed; ‘exposure to ridicule’ or
‘vulnerability to litigation’ [syn: exposure]
2: susceptibility to injury or attack [ant: invulnerability] (Webster online)
Main Entry: risk
Pronunciation: ‘risk’
Function: noun
Etymology: French risque, from Italian risco
1: possibility of loss or injury: PERIL
2: someone or something that creates or suggests a hazard
3a: the chance of loss or the perils to the subject matter of an insurance
contract
also: the degree of probability of such loss b: a person or thing that is a
specified hazard to an insurer <a poor risk for insurance> c: an insurance
hazard from a specified cause or source <war risk>
Main Entry: vul·ner·a·ble
Pronunciation: ‘v&l-n(&-)r&-b&l, ‘v&l-n&r-b&l
Function: adjective
Etymology: Late Latin vulnerabilis, from Latin vulnerare to wound, from
vulner-, vulnus wound; probably akin to Latin vellere to pluck, Greek oulE
wound
1: capable of being physically wounded
2: open to attack or damage: ASSAILABLE
3: liable to increased penalties but entitled to increased bonuses after winning
a game in contract bridge
From this perspective, a system adaptively responds to perturbations by showing
a typical stress reaction—potentially source of dysfunctions ranging from reversible operational malfunctions to reversible or irreversible structural changes—
which may lead to alteration of the system’s topology and, eventually, to a total
destruction (physical or operational). This perspective is an expression of a possible
physiological model of vulnerability in which a system vulnerability is a threat, a
predictive quantity reflecting system’s selective stress reaction toward a respective
threat.
An examination of the cybernetic, sociologic, semantic, and physiologic interpretations of the vulnerability, as well as those found in literature, suggests the
96
5 The Vulnerability Issue
following methodological propositions and corollaries—considered to be both
decent and adequate to the on-going emerging and consolidating research.
Table 5.1 elaborates on the suggested propositions and corollaries at the methodological level.
Table 5.1 Vulnerability-related propositions and corollaries for methodological approach
Proposition/corollary
Description
Relevant notes
Proposition 1
Risk and vulnerability are
distinct notions addressing
complementary realities of
systems behavior:
• Threats (hazards)—represent in
a generic way sources or causes
of potential losses, damages, and
injuries
• Exposure to the threats
• Subject(s) of the threat
The specific difference between
risk and vulnerability comes
from the following observations:
• Risk addresses the threats
(sources/causes), characterizing
the consequences of their
occurrence
(losses/damages/injuries), the
perception on the consequences
(subjectivity) and the frequency
(probability) of occurrence
• Vulnerability addresses the
subject(s) of the exposure to
threats, characterizing the type
and level of susceptibility, the
reaction to stress or the subject’s
propensity to support the
exposure to the threats
occurrence
Due to Proposition 1,
vulnerability of subjects is (has
to be) read as the system’s
vulnerability
Due to the variety of paths
(channels) of subject(s) exposure
to threats, it is believed that, in
order to satisfy stakeholders’
different opinions and angles of
evaluation, only the adoption of
an alternative set of approaches
to vulnerability is adequate
The three categories of threat,
exposure, and subject should be
seen as consubstantial with the
system
Proposition 2
Corollary 1
Corollary 2
5.1 Definitions and Conceptualization
97
In light of the foregone discussion, authors derive the definition of vulnerability
that also represents our posture on the topic. This definition is adopted for the
reminder of current discussion:
Definition 1 System’s vulnerability to a threat is a predictive quantity reflecting
system’s selective stress reaction toward a respective threat.
5.2
Methodological Aspects in Quantitative Vulnerability
Assessment in Transport Systems
Methodologically, vulnerability assessment finds itself in a defining and formalizing time (i.e., see, Musser (2002) and Bibliografie in Vamanu (2006)). The proposed approach for a quantitative vulnerability assessment takes root from thoughts
and ideas in scientific literature, official documents, and statements from international and/or reference country national regulatory bodies such as the USA and the
EU, as well as best practices as postulated by experiences of the current authors.
Moreover, it is our intention that the vulnerability assessment models and methods
would become a natural extension of risk assessment especially for those interested
in hazmat transportation. Consequently, one might notice the risk-specific ideas,
which have been borrowed, whenever suitable, to enhance the proposed vulnerability assessment models.
The suggested methodology follows the generic ‘complex systems vulnerability
assessment flow chart’ as introduced by the US Department of Energy (USDoE
2001). Figure 5.4 is developed from this flow chart and provides the methodological aspects acting as guidance in developing a transportation corridor vulnerability assessment models in the current text.
Fig. 5.4 Phases of vulnerability assessment, adapted and modified from USDoE (2001)
98
5 The Vulnerability Issue
5.2.1
Transportation System Definition
The ‘Transportation System’ is defined in accordance with the interpretation given
in the preceding chapters with an emphasis on the statement ‘the System is the
Whole.’ Thus, a transportation system is viewed consisting:
• the rolling infrastructure (road and railway networks);
• the transportation infrastructure (transportation fleet);
• the geographical, social, economic, and political characteristics of the
environment;
• traffic actors;
• population coming in contact with the transportation segment;
• the interconnections with other systems.
It is essential to recall that any of the aforementioned components may be
considered as threat source, threat target, or exposure path (channel) within the
current view of system–risk perspective. To illustrate, a rolling infrastructure is
(i) a source of threat when taking into account that a precarious quality (e.g., a
pothole or damaged tracks) could result in an increased frequency of accidents;
(ii) target of the threat when subject of an attack intended to ‘harm’ the transportation segment (i.e., putting a rolling infrastructure into an inoperable state); and
(iii) exposure path when it is used in an instance of moving a radioactive cargo
inside a city in order to detonate it.
The threats to the system are classified from the source point of view as internal
and external. The threats are considered to be those actions (intentional or not) or
system states that can have negative effects on targets (Krömker 2001); the sources
may be or come from:
•
•
•
•
•
•
economical
environmental
infrastructure
political
personal
social.
5.2.2
Defining the System by Indicators
The approach of defining the system by the characteristic indicators is adopted in a
methodological phase. Accordingly,
1. a system is the expression of all its properties, expressed by indicators; and
2. an indicator is an algebraic, Boolean, or semantic variable that assigns metrics
(unit and evaluation scale) to the expressed property.
5.2 Methodological Aspects in Quantitative Vulnerability Assessment …
99
Mapping the system onto the set of its characteristic indicators creates an
information resource that goes beyond the needs of risk and vulnerability assessment. In the final analysis, any information about the system can be derived from
only that information resource. The ultimate goal of having the set of indicators
containing ‘everything about the system’ is not a reasonable expectation. Moreover,
in practice, this may prove counterproductive since it would lead to excessively
lengthen the assessment oriented toward clear-cut objectives: including efficiency,
security, risk, and vulnerability. As a direct consequence, providing (identifying)
the proper, well-defined set of indicator characteristic/representative for a given
system becomes a key issue involving a great deal of responsibility—both from the
technological and from the deontological viewpoints. Therefore, the set of indicators should hold ‘everything, in as much as feasible possible, about the system that
is relevant to a given assessment target.’
In recent times, indicators have been used within social planning area for
assessing—in the most cases—the disruptive events that may have environmental
negative effects. In such a context, an indicator can be defined as an event, expression, or tool which characterizes a phenomenon. Identification and assessment
of events occurring in systems with high level of complexity can be straightforwardly done using indicators, under a proper choice of representative parameters
(Boverket 2007). The use of indicators also makes possible the identification and
definition of requests and goals or program and action planning regarding a
specific system or activity.
Defining the systems by indicators is a common method in the vulnerability
assessment of complex systems (Brooks et al. 2005; Krömker 2001). Therefore, the
analytical building of the generic Transportation System comes down to defining
the relevant indicators set. The indicators should be chosen in accordance with the
reference requirements. These requirements include:
•
•
•
•
the
the
the
the
indicator
indicator
indicator
indicator
must
must
must
must
be
be
be
be
quantifiable;
relevant to the process/phenomenon being address;
relevant to the final goal of the assessment;
convenient in regard to geographical and time scales.
It has also been suggested that vulnerability of a road transportation system
should be given in terms of susceptibility to incidents that may lead in considerable
reduction in road network serviceability (Berdica 2002). The same author also
introduces reliability for describing adequate serviceability under the operating
conditions encountered at a given time. The validity of this approach is more
obvious in the case of railway transportation systems.
However, in the current methodological phases, authors will assume that there
are two contributors to the vulnerability of the transportation system: (1) internal
vulnerability and external vulnerability factors. Internal vulnerability is given by the
intrinsic characteristics of the system such as the rolling infrastructure, the transportation fleet, and geographic characteristics. The external vulnerability comes
from the interactions of the transportation system to other systems including but not
100
5 The Vulnerability Issue
limited to medical system, emergency response system, population, market, and
stock exchange markets.
The contributors should not be seen as disjoint entities, but rather as interacting
and influencing each other—which enables the consideration of dependencies and
interdependencies. The indicators set must be defined so as to reflect these
dynamics. This approach is highly recommended and is found in literature (Kaly
et al. 2003) and applied in regulatory recommendations and normative documents
on risks and vulnerabilities in the chemical industry sector (European Commission
1996a, b, c). Indicators also have to define and meet the following requirements
(Childs et al. 2000; European Commission 1996a, b, c; Papadakis and Amendola
1997):
• to characterize the system operational environment, including information as
geographical position, meteorological, hydrological, geological data … and,
when necessary, historical;
• to reflect the potential sources of risk;
• to be capable of reflecting the areas of a high risk of occurrence of disruptive
events;
• to reflect the interaction with the other connected systems, including ‘services’;
• to take into account the relevance radius—the impact radius (i.e., distance up to
which an event spreads its effect) of a potential emergency involving hazardous
materials;
• to take into account the rolling infrastructure and its quality;
• to take into account the population coming in contact with the transportation
system (potentially exposed to a disruptive event);
• to take into account the emergency response capability.
5.2.3
The Vulnerability Assessment of Transportation
System
Starting from the previous definition, the following approach is adopted for vulnerability assessment of transportation systems:
1. Describe the transportation system by indicators. The indicators are identified
and analytically defined in such a manner as to (i) satisfy the generic requirements of defining indicators, (ii) characterize (express) the constituent components of the transportation system as suggested in Chap. 4, and (iii) reflect, as
realistically as feasible, the operations and operability of the transportation
system within the context of a system of systems—a system interacting with
other systems.
2. The transportation segment (i.e., the route of interest) is divided into measurement points.
5.2 Methodological Aspects in Quantitative Vulnerability Assessment …
101
3. Vulnerability is assessed at every measurement point, taking into account the
particular spatial and environmental characteristics.
4. After ‘running through’ and assessing the whole transportation segment, one
gets the segment’s vulnerability profile.
5. The segment’s Vulnerability Index is then computed from the vulnerability
profile.
6. The vulnerability indices of the transportation segments are contributors to the
Vulnerability Index of the Transportation System.
7. Vulnerability of a given system at a measurement point is assessed by taking
into account the operational environment of the system. In a neighborhood, this
is described by a circular area centered on the measurement point and having a
radius equal to the relevance radius (Rrel). The relevance radius is the distance
up to which an event involving hazardous materials extends its effect and is
either computed by (i) performing procedures for LOC consequence assessment
or (ii) obtained from statistics or using expert judgment.
8. The approach is adopted, by analogy and with risk deontology— As Resilient As
Society Permits (ARASP) concept (Gheorghe and Vamanu 2006a, b); this
permits the analyst to define the acceptability levels for vulnerability according
to his perception, belief system, and or objectives. Thus, System Vulnerability
Index places the system in one of the three acceptability basins: (1) minimal,
(2) acceptable, or (3) unacceptable vulnerability. Notice that, with respect to the
analyst or preferences of the stakeholder, defined in terms of perception, interest,
etc., the same transportation system may be placed in different acceptability
basins.
All proposed models share several quantities. These shared quantities are presented in Table 5.2.
The current authors suggest that the proposed approach offers several advantages. These advantages including:
• The approach is suitable for optimal routing selection by comparative assessment of different transportation options.
• It allows the identification of the sensitive sections of a transportation segment.
• It ensures prioritization targeting for the vulnerability mitigation.
• It favors a sound definition and development strategies in the context of sustainability and viability for rolling infrastructure, communities, and industrial
and agricultural sectors
• It favors security ensuring decision-making processes.
• It contributes to the improvement of emergency response systems.
• The approach incorporates viewpoints of different stakeholders and therefore
favors cost minimization.
• It provides the capability for assessment at different level of detail—incorporation of different measures.
The presented vulnerability assessment expresses the purpose of expanding the
horizon of risk assessment to include the influence of the other interconnected
102
5 The Vulnerability Issue
Table 5.2 Proposed shared quantities among models for transportation of dangerous goods
Quantity
Description
Rrel
Relevance radius. When using more than one relevance radii as in the instance
when considering a relevance radius for each potential physical effect of loss of
ðiÞ
containment, Rrel shall be written Rrel sau RðiÞ
rel effect
hi
D(P1, P2)
Measurement point elevation
The geographical distance (measured on great circle) between locations P1 and
P2; the locations are given by their geographical coordinates (longitude, latitude)
The distance between the measurement point and the closest town (populated
place)
Number of towns within the relevance radius
The average radius of a town; in most cases, the towns (populated places) are
provided as point features of a GIS layer. In the proposed models, a town is
assumed as covering a Rtown circular area. Obviously, if a detailed GIS is
available, characteristic town data should be used
The distance between the measurement point and the closest city
Number of cities within the relevance radius
The distance between the measurement point and the closest river
The distance between the measurement point and the closest water body
(including lakes)
The number of water bodies within the relevance radius
The number of rivers within the relevance radius
The distance between the measurement point and the closest airport
The number of airports within the relevance radius
The distance between the measurement point and the closest high-voltage line
The number of high-voltage lines within the relevance radius
The number of high-voltage lines crossed by the road/track segment between the
current and previous measurement points
Vegetation at measurement point
Boolean variable; True if the measurement point inside a potentially floodable
area
The type of the rolling infrastructure
The quality of the rolling infrastructure
The seismical risk at the measurement point
The number of bridges crossed by the road/track segment between the current
and previous measurement points
dtown
Ntown
Rtown
dcity
Ncities
driver
dwb
Nwb
Nrivers
daip
Naip
dHV
NHV
NHV_crossed
Veg
Flood
Rtt
Rtq
Eq
Nbridges
systems, as well as components from non-physical systems (Nagel and Rasmussen
1994). The proposed approach should be seen as taking distance to the assessed
system/process in order to get a synoptic view of a playground, as seen from the
perspective of an actor.
Purposefully, this research took three quantitative vulnerability assessment
methods and presented them in the sequel to: (1) point out ways to approach the
issue of vulnerability in complex systems, (2) illustrate a possible approach to
5.2 Methodological Aspects in Quantitative Vulnerability Assessment …
103
vulnerability assessment for transportation systems, and (3) offer a glimpse to
readers into how conceptual considerations can be translated into analytical and
numerical models. The selected methods are based on the Index and Matrix Models
which have an origination in the Scandinavian School (Nilsson et al. 2001) and the
generic model of Quantitative Vulnerability Analysis (QVA) which addresses
structural vulnerability (Gheorghe and Vamanu 2004).
In the following chapters, the description of the aforementioned models and
methods are presented, first in a generic form and then adapted and implemented for
transportation system vulnerability assessment.
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the European Communities. Retrieved from http://ec.europa.eu/dgs/home-affairs/what-we-do/
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and distribution of governmental economical means at the local authority level. Lund, Sweden:
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to meet the requirements of council directive 96/82/EC (Seveso II). Luxembourg City,
Luxembourg: EC: Joint Research Centre.
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analyzing critical infrastructure interdependencies. IEEE Control Systems, 21(6), 11–25. http://
doi.org/10.1109/37.969131
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Tokgoz, B. E. (2012). Probabilistic resilience quantification and visualization building
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Washington, DC: U.S. Department of Homeland Security. Retrieved from www.dhs.gov/
xlibrary/assets/nipp-ssp-national-monuments-icons.pdf
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methodology (p. 15). Washington, DC: U.S. Department of Energy—Office of Energy
Assurance. Retrieved from https://hsdl.org/?view&doc=140176&coll=limited
Vamanu, B. I. (2006). Managementul riscurilor privind transportul substanţelor periculoase:
aplicaţii ale sistemelor dinamice complexe (Dissertation). Universitatea Politehnica Bucureşti,
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Bucureşti.
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Chapter 6
Consensus-Driven Models for QVA
in Transportation Corridors
Abstract In this chapter, two consensus-driven methods, the Index Method, and
the Relevance Matrices Method, for quantitative assessment of vulnerability in
transportation systems, are discussed. These methods are derived from Nilsson,
Magnusson, Hallin, and Lenntorp’s work: Models for vulnerability auditing and
distribution of governmental economical means at the local authority level (Nilsson
et al. in Models for vulnerability auditing and distribution of governmental economical means at the local authority level. Lund University Centre for Risk
Analysis and Management (LUCRAM), Lund, Sweden, 2001).
6.1
The Index Method
This model targets assessment of the vulnerability level, described by Vulnerability
Index, based on a set of quantifiable and measurable parameters describing the
authority (management) efficiency. The model draws upon the following logic:
• The concept of vulnerability has a direct relationship with the notion of ‘failure’
to comply with the adopted ‘policy.’
• The Policy Compliance Index is obtained as a weighted sum of instrumental
indicators/parameters attached to the instrumental monitors.
• The instrumental indicator values are obtained either by ‘direct democracy’
means (e.g., public consultation, polls, Delphi polls, expert auditing) or analytical methods.
• The weights pondering instrumental indicators contribution to the Policy
Compliance Index are computed from relevance indices of (1) the strategies to
the policies, (2) partial objectives to strategies, and (3) instrumental indicators
to partial objectives. These are provided in a form of matrix.
• The vulnerability index of a system of interest, with respect to complying level
of the adopted policy, is computed based on the relevance weights of the
instrumental indicators and the instrumental indicators themselves.
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_6
107
108
6 Consensus-Driven Models for QVA in Transportation Corridors
Table 6.1 Five hierarchical levels of indicators for vulnerability
Level
Description
Level 1—Final Goal
Level 2—Strategic
Authorities (system management) adopted policy
Contains the targets that must be reached in order to reach the final
goal (i.e., long-term strategic goals)
Holds the actions that should be performed to reach the objectives at
the strategic level. Each strategic target includes a number of
operative partial targets. When combined, these reflect the level up
to which the strategic targets are reached
Indicators at this level are referred to as base indicators. These are
the parameters which, together, define the level of compliance of the
partial operational objectives
The instrumental parameters must be provided with numerical
values. The possible sublevels of the operational level contain
parameters used for the computation of the base indicators
Level 3—Operational
Level 4—Instrumental
Level > 4
6.1.1
Designing the System
The system is described by indicators. These indicators are classified into categories and placed on corresponding hierarchical levels. The parameters at a level
are connected with the parameters at the upper level, based on relevance criteria.
The Vulnerability Index is computed in consideration of the value of the topmost
indicator.
The number of levels may vary depending on the complexity of the system of
interest. However, there are five minimum required numbers of levels. Table 6.1
provides a description of the minimum required number of levels.
6.1.2
The Risk-Management Capability Index and Weights
Computation
As mentioned before, the target of this method determines the vulnerability of a
system as an expression of the system capability of mitigating or managing risks.
For system described above, risk-management capability index, I, is computed as:
I¼
np
X
Wi Xi
ð6:1Þ
i¼1
with
Wi the computed weights of the instrumental parameters (the method is described
later in this chapter)
6.1 The Index Method
Xi
np
109
the numerical values (0, …, 5) of the instrumental parameters Pi
number of instrumental parameters/indices.
6.1.2.1
Weights Computation
One should notice that the parameters from the instrumental level have different
importance (relevance) in complying with the partial objectives described by the
operational indicators. Additionally, the contribution of the operational indicators
to each of the strategic goals is different and, in turn, the strategic objectives
differently contribute to the success of the long-term policy. In other words, the
intermediate weights should be defined in order to get the final weights vector, Wi,
which directly link system parameters to the risk-management capability index. The
intermediate weights characterize the connections between each element at a
specific level and all the elements from the lower level. In subsequent sections, the
intermediate weights are referred to as level weights.
Keeping this information in mind along with the consideration of Eq. (6.1), the
following two arise: computing the level weights and computing the final weights
vector Wi.
6.1.2.2
Computing the Level Weights
There are several ways that could be used to determine level weights. In this
research, authors consider an approach suggested by Nilsson et al. (2001)—The
Delphi polls (Kerr 2001).
Perhaps the most challenging questions for panel members in the Delphi poll
approach are in the form: Given an operative target Om, (m = 1, …, no, with no—
number of operative targets) and a number of npi instrumental parameters, how
would you weight these parameters on a 0–5 scale knowing that Om is defined as:
Om ¼ cm;1 p1 þ cm;2 p2 þ cm;3 p3 þ . . .cm;npi pnpi
ð6:2Þ
with
ci,j the level weights;
i = 1, … no; j = 1, …, np.
pj parameters;
j = 1, …, np.
Consequently, in order to obtain level weights, one must apply the above process
starting from the system bottom levels while moving toward the topmost levels.
110
6 Consensus-Driven Models for QVA in Transportation Corridors
6.1.2.3
Computing the Final Weights
The following describes how the final weights vector is determined starting from
the intermediate weights. The algorithm is characteristic for the 4 levels in a system
of interest. However, in the case of additional levels, the procedures remain the
same.
The Delphi poll results are:
(i) the intermediate weights between the instrumental and operational levels (C)
5
P
c1;1 p1 þ c1;2 p2 þ c1;3 p3 þ c1;4 p4 þ c1;5 p5 ¼
c1;i pi ¼ O1
i¼1
5
P
c13;1 p1 þ c13;2 p2 þ c13;3 p3 þ c13;4 p4 þ c13;5 p5 ¼
c13;i pi ¼ O13
i¼1
5
P
c17;1 p1 þ c17;2 p2 þ c17;3 p3 þ c17;4 p4 þ c17;5 p5 ¼
c17;i pi ¼ O17
ð6:3Þ
i¼1
or, in the matrix form:
0 1
1
p1
1
0
c1;1 . . . . . . . . . c1;5
O1
B p2 C
C B C B . C
B
... ... ...
C B p3 C ¼ @ . A
B
.
A B C
@
... ... ...
@ p4 A
O17
c17;1 . . . . . . . . . c17;5
p5
0
ð6:4Þ
or, in the short form:
O¼CP
ð6:5Þ
(ii) the intermediate weights between the operational and strategic levels (D)
S1 ¼
17
X
d1;i Oi
i¼1
S2 ¼
17
X
d2;i Oi
i¼1
S3 ¼
17
X
i¼1
d3;i Oi
6.1 The Index Method
111
or
S¼DO
with
0
1
d1;1 . . . . . . . . . d1;17
A
... ... ...
D¼@
d3;1 . . . . . . . . . d3;17
From the above, one gets:
O¼CP
S¼DO
ð6:6Þ
I ¼ES
Considering the previous results, the risk-management capability index is
obtained as:
I ¼ E S ¼ E D O ¼ E D C P ¼ WP
ð6:7Þ
with
W ¼ E D Cbeing the final weights vector
w ¼ ðW1 ; W2 ; W3 ; W4 ; W5 Þ
The symbolic equation of computing the final weights is given in Fig. 6.1.
6.1.2.4
Assessment Results: The Vulnerability Index
The final weights Wi are normalized to 1 in order to get a relevant result in terms of
comparative vulnerability assessment as well as a qualitative information on the
system vulnerability. This is done in accordance with Eq. (6.8).
Fig. 6.1 Final weights vector computation symbolic equation
112
6 Consensus-Driven Models for QVA in Transportation Corridors
np
X
wi ¼ 1
ð6:8Þ
i¼1
from:
I¼
np
X
wi X1 ¼ 1
ð6:9Þ
i¼1
I¼
np
X
wi ¼ 1
i¼1
0 Xi 5
one gets
0I 5
The System’s Vulnerability Index (V) is defined with respect to the risk-management capability index as indicated in Gheorghe and Vamanu (2003):
I
V ¼ 100 1 5
ð6:10Þ
Notice that from Eq. (6.10), the system’s vulnerability is defined over a scale of
0 to 100 with V ¼ 0 corresponding to a non-vulnerable system. V ¼ 100 expresses
system in a totally vulnerable state.
6.1.3
The Index Method: Transportation Corridor
Vulnerability Assessment
This section contains a model intended to indicate the feasibility of applying the
Index Method in the field of hazmat transportation. The natural compatibility
between the generic model described above and the general problematique situation
of vulnerability of transportation systems is thought as being evident.
The suggested model is driven by the following assumptions:
• The Transportation Corridor (Segment) is characterized at every measurement
point by temporal, spatial, political, and social aspects of the vicinity of the
transportation segment which is a closed operation environment. These features
named as location features and they characterize the assessment point.
• The Transportation System is analytically defined by indicators and the interactions between the indicators.
6.1 The Index Method
113
Table 6.2 Elements of the proposed model
Elements
Description of elements
The
organizer
The object
The goal
National Transportation Authority
Vulnerability assessment of a transportation system
(i) Determining the level of capability in managing the risks induced by a
transportation activity
(ii) Identifying and gathering relevant data for short-term policy making in
transportation sector. The objective is to optimize the national capabilities in
terms of (a) business, (b) safety, and (c) emergency planning and response
• The input values (Xi) of the instrumental parameters (Pi) are computed function
of the location features.
• The level weights (Ci,j) between the operational and instrumental levels reflect
the logical relationships between the instrumental and operational indicators and
are considered constant during the assessment.
Let us denote Xi ð Þ as the function returning the value of the instrumental
parameter Xi. The model is developed in consideration of the Organizer, the Object,
and the Goal. Table 6.2 elaborates on the description of Organizer, Object, and
Goal.
6.1.3.1
System Description by Indicators and Classification Structure
The indicators have been chosen in accordance with the basic principles of the
transportation systems vulnerability assessment as indicated in Sect. 5.2.3. The
indicators are classified based on four levels: Final Goal, Strategic, Operational,
and Instrumental.
The Final Goal is Optimizing the transportation system from the vulnerability
viewpoint. This model assumes that the vulnerability of the transportation system is
given by social, ecological, and economic factors. These are reflected at the
Strategic level and are indicated in terms of:
S1
S2
S3
S4
S5
S6
Providing consumer supply and traffic fluency;
Emergency prevention;
Providing the emergency response management capabilities;
Secure the transportation activity from the FINANCIAL viewpoint;
Secure the transportation activity from the CITIZEN viewpoint;
Secure the transportation activity from the ENVIRONMENTAL viewpoint.
Notice that S1–S6 also correspond to the three targets of the assessment, namely
business, safety, and emergency.
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6 Consensus-Driven Models for QVA in Transportation Corridors
The Operational Level has 19 indicators:
O1
O2
O3
O4
O5
O6
O7
O8
O9
O10
O11
O12
O13
O14
O15
O16
O17
O18
O19
Providing intelligent traffic control and guidance systems;
Ensuring roads/railways quality;
Residential areas avoidance;
Providing theft/robbery protection (physical and/or financial);
Ensuring the quality of the transportation vectors (lorry, train, etc.);
Ensuring the intervention capability of the emergency teams;
Ensuring the intervention capability of the medical personnel;
Ensuring the intervention capability of the firefighters;
Providing evacuation routes;
Providing the intervention routes;
Highly populated areas avoidance;
Flood prone areas avoidance;
School/kindergarten areas avoidance;
Public institutions area avoidance;
Highly industrialized areas avoidance;
High seismic risk area avoidance;
Providing ‘unstressful’ routes;
High accident risk areas avoidance;
Consequence minimization in the case of accident.
Similar to strategic objectives, the range of O1–O19 expresses indicators which
affect the performance at each of the operational levels and are related to least one
strategic objective.
The Instrumental level has 26 indicators. The indicators at this level are the input
data source of the model. The indicators have been defined in such a manner as to
allow a numerical value being computed based on publicly available data as indicated Appendix C or in Vamanu (2006). The 26 indicators at this level are:
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
P12
P13
Periodic checking, control, and maintenance procedures (road/railway quality);
Periodic checking, control, and maintenance procedures (hazmat transportation vectors quality);
Assessing and following the urban development dynamics;
Instruction, formation, and periodical verification of personnel (emergency
teams)
Instruction, formation, and periodical verification of personnel (medical);
Instruction, formation, and periodical verification of personnel (firefighters);
Public information and instruction;
Periodical emergency exercises;
Safety-culture;
Distance toward the closest town;
Number of towns within the relevance area;
Distance toward the closest city;
Number of cities within the relevance area;
6.1 The Index Method
P14
P15
P16
P17
P18
P19
P20
P21
P22
P23
P24
P25
P26
115
Rolling infrastructure type (road, railway, details);
Floodable area;
Vegetation;
Distance toward the closest water body (river, lake, etc.);
Presence of auxiliary routes;
Transportation segment type (urban/extraurban);
The presence of traffic control and surveillance systems;
Rolling infrastructure quality
The distance toward the closest airport;
Number of airports within the relevance area;
Segment’s slope;
Seismic risk level at the current location;
‘Sensitive’ objects at the current location.
On the Selection of the Indicators
A close examination of each of the indicators above, it is easy to surmise these
indicators follow a ‘natural’ logic. However, there might exist cases in which more
detail on the logic of indicator selection is need.
Specifically, a first glance at P4, P5, and P6 suggests that the three indicators refer
to the same indicator (i.e., Instruction, formation, and periodical verification of
personnel). However, the difference is articulated in the reference target (i.e.,
medical, firefighters, emergency, and intervention personnel, respectively). This is
an example of a typical situation in which sublevels are needed. This situation could
be represented as T and containing the three aforementioned indicators. The T
indicators would be in this case the parameters for a single value of one of the P
level indicators reflecting Instruction, formation, and periodical verification of
personnel. Following the same reasoning, the value of each of the T level indicators
may be computed from three other indicators (Instruction Level, Formation Level,
Verification Level) placed on a sublevel U of the T level. The rationale behind the
current approach is (i) keeping a relatively small complexity of the system and
(ii) preserving the same four-level structure of the system, as in the generic model,
and subscribing to systems theoretic principle of recursion (Clemson 1984; Hester
and Adams 2014).
In literature, safety-culture addresses the attitude within an organization toward
achieving the duties associated with security. Initially introduced in the nuclear
realm after the Cernobil accident, the notion typically refers to ethics, value, and
attitude of individual members within a given system (i.e., organization). In the
present case, P22 reflects the same notion as transposed to the case of a hazmat
transportation situation. An equivalent though in terms of risk assessment could be
described as: an accident may occur in case of an improperly loaded cargo, due to
the low level of ‘safety-culture’ within the shipping company.
A final indicator of interest is O17. Providing ‘unstressful’ routes. This indicator
contributes to the transportation system vulnerability component induced by the
116
6 Consensus-Driven Models for QVA in Transportation Corridors
driver (traffic participants) behavior in traffic. The interest here is to ensure that
proper attention is paid towards the psychological aspects of participants in traffic.
O17 is an important variable; previous researches involving psychology, statistics,
and surveys have suggested that factors like quality of the rolling infrastructure,
traffic density, meteorological conditions or too many traffic surveillance and
restrictions directly influence the actions and behaviors of people in traffic
(e.g. Barjonet 2001). In short, it can be considered that stress leads to anxiety, lack
of attention, and the decrease of the overall driver’s physiological performances
which, in turn, could be a source of an accident.
6.1.3.2
Transportation System Vulnerability Assessment
A reminder is necessary. The value of each indicator at a given level is dependent
on at least one indicator from the previous level. In other words, achieving an
objective at one level depends, to a certain degree, on achieving one or more
objectives on the previous level. Figure 6.2 attempts to capture this logic (linkage)
between levels of a system of interest.
Computation of the Instrumental Parameters
The list below enumerates only the input values (Xi) of the instrumental parameters
(Pi) whose computation relies on the particular location along the transportation
segment (i.e. the measurement point). For each of these, the computation
assumptions together with the accompanying equation is provided.
All the other (e.g. X1 – X9) are assumed as constant and given from statistics /
expert judgement.
X10 = distance to the closest town
Fig. 6.2 Logic and relationship between system indicators
6.1 The Index Method
117
Computed by linear interpolation, as a function of Rrel, Rtown, and dtown.
(
X10 ðRrel ; Rtown ; dtown Þ ¼
0
5; for dtown [ d
dtown d 00
5
; for dtown d 0
d0
ð6:11Þ
with
d′ = Rrel + Rtown
d″ = min(Rrel + Rtown).
Variables d′ and d″ are introduced to take into account the case when
Rtown < Rrel. Thus, by using Eq. (6.11), one gets X1 = 0 (worst-case) even though
dtown > 0 (the whole town is inside Rrel).
X11—towns within Rrel
X11 ðNtown Þ ¼ ct
ð6:12Þ
X12—distance to the closest city
Computed by linear interpolation, as a function of Rreland dtown.
(
X12 Rrel ; dcity ¼
5;
5
dcity
Rrel
for dcity [ Rrel
; for dcity Rrel
ð6:13Þ
X13—cities within Rrel
X13 ðNcities Þ ¼ ct
ð6:14Þ
X14—The rolling infrastructure type
Constant, depending on the rolling infrastructure characteristics (e.g., singleversus double-lined street, highway, etc.).
X14 ðRtt Þ ¼ ct
ð6:15Þ
X16—Vegetation
Constant, depending on the vegetation at the measurement point.
X16 ðVegÞ ¼ ct
ð6:16Þ
X17—distance to an important water (creek, river, lake, etc. )
Computed by linear interpolation, as a function of Rrel, driverand dwater.
(
X17 ðRrel ; driver ; dwater Þ ¼
5; ;driver Þ
5 minðdwater
;
Rrel
for minðdwater ; driver Þ [ Rrel
for minðdwater ; driver Þ Rrel
ð6:17Þ
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6 Consensus-Driven Models for QVA in Transportation Corridors
X19—Transportation segment type (urban/extra)
X9 dcity ; dtown ¼ ct
ð6:18Þ
P19 = X19 reflects the vulnerability component induced by the possibility of
occurrence of pedestrian-involving accidents. Hence, the value of X19 must be
chosen in manner that reflects a more vulnerable situation when the measurement
point is inside an urban area.
X19 dcity ; dtown ; Rtt ¼ ct
ð6:19Þ
X20—Presence of the traffic surveillance and control systems
X20 must reflect a higher vulnerability in a situation in which traffic surveillance
and control systems (cameras, radars, traffic signs, traffic lights, etc.) are fewer.
X22—distance to the closest airport
Computed by linear interpolation, as a function of Rrel and daip.
(
X22 Rrel ; daip ¼
5;
5
daip
Rrel
for daip [ Rrel
; for daip Rrel
ð6:20Þ
X23—Airports within the Rrel
X23 Naip ¼ ct
ð6:21Þ
hcp hcp1
X24 hpc ; hpc1 ¼ D Pcp ; Pcp1
ð6:22Þ
X24—The segment slope
with
Pcp
Pcp−1
hcp, hcp−1
current measurement point (location)
previous measurement point (location)
elevations at the current and previous measurement points,
respectively
D(Pcp, Pcp−1) the distance between the previous and the current measurement
points (in fact, the assessment resolution).
X25—Seismic risk at the current location
X25 ðEqÞ ¼ 5 X26—‘Sensitive’ objects at current location.
Eq
2
ð6:23Þ
6.1 The Index Method
119
In this model, the following ‘sensitive objects’ are taken into account: the
bridges, the crossings between the transportation segment and the high-voltage
lines, cities and towns passing-through, and the vegetation type.
X26 Nbridges ; NHV ; Veg; dcity ; dtown
!
1 w01 g0 Nbridges þ w02 g0 ðNHV Þ
¼5 þ w03 g0 ðVegÞ þ w04 g0 dcity þ w05 g0 ðdtown Þ
ð6:24Þ
with g′ defined as:
g0 : ½0; 1 ! R; and:
8 1
< 5Nbridges ; for Nbridges \5
g0 Nbridges ¼
1;
for Nbridges 5
:
0;
for Nbridges ¼ 0
8
< 3N1 HV ; for NHV \3
0
g ðNHV Þ ¼
1;
for NHV 3
:
0;
for NHV ¼ 0
g0 dcity ¼
g0 ðdtown Þ ¼
g0 ðVegÞ ¼
1; for measurement point inside a city,
0; otherwise:
1; for measurement point inside a town,
0; otherwise:
1; for measurement point inside a forest area;
0;
otherwise:
and w0i¼1...5 are the respective relevance weights of each g′.
In this model, X1,…,9,15,18,21 are considered as being given by expert judgment
(i.e., using Delphi polls).
Naturally, in a more complex models, (some of) the values of X1,…,9,15,18,21 may
also be obtained either analytically or by extending the indicator levels of the
system of interest. At the same time, other indicators may prove valuable when
considering international transportations. Values of those indicators may depend for
instance by elements as the National Gross Product or the GEM-E3 model’s
Country Index as indicated in Ciscar et al. (2004).
120
6.2
6 Consensus-Driven Models for QVA in Transportation Corridors
The Relevance Matrices Method
An alternative procedure for assessing vulnerability in each measurement point of a
transportation corridor is The Matrix Method. As previously stated, this method
originates from Nilsson et al. (2001) research which addresses municipal management. Yet, the same scheme, as it will be shown, is also suitable assessing
vulnerability of the transportation corridors.
Originating from the same school of thought as the Index method, the Matrix
Method derives a ‘robustness index’ of an assessed system by consensus-driven
quantification of the risks, the system is prone to, and risk-management capability,
of the system managerial staff. The System Vulnerability/Robustness is assessed
against on a set of acceptability criteria defined by upper and lower thresholds.
Vulnerability is given (rendered) in a space defined by the risk (Ox) and the
risk-management (mitigation) capability (Oy). Three acceptability basins are
defined within this space as unacceptable, tolerance, and acceptable. Figure 6.3
illustrates x–y plan for Ox and Oy along with the three basins of vulnerability.
The system is characterized by three indices: I1—reflecting the maximum level of
risk (threat) the system is exposed to; I2—the current risk level of the system; and
I3—the current level of risk mitigation capabilities. Furthermore, I2/I1 reflects the
relative risk level the system is exposed to; I2/I1 is the quality of the
risk-management (mitigation) capabilities of the system governing entity (i.e., local
authority, corporate management). The system’s robustness and resilience gets
higher as I3/I2—a dynamic variable of the system—gets closer to 1.
Relevant information for vulnerability assessment is provided by the graphical
rendering of the results. Thus, the risk profile points out the most sensitive areas that
Fig. 6.3 System localization in vulnerability space
6.2 The Relevance Matrices Method
121
have to be addressed in order to reduce the overall system vulnerability. This is, in
fact, a direct consequence of one of the strongest points of this method—the
capability of individual risk mitigation assessment. In the same line, placing the
system in one of the acceptability basins is straightforward and meaningful way of
visually communicating vulnerability assessment results in a simple manner.
Additionally, comparative assessments of ‘what-if’ scenarios or system evolution in
time can gain more relevance when represented in risk/risk mitigation matrix.
In the following section, the basic equations and analytical foundation of a
modified version of the general assessment method are presented. This is followed by
a model tailored for transportation systems which goes on top of the generic method.
6.2.1
The Method
The relevance matrix method encloses six phases:
Phase 1
Identification and definition of (i) the risk types (threats, dangers) the system is
prone to, and (ii) the possible effects related to each risk type (i.e., consequences—
defined in terms of losses to the ecological system, human lives, or private property
losses). Immediate results are the risk and loss classes.
Let us denote:
RTi—risc type i;
LTk—loss type k;
i = 1…nr, nr = the number of the identified risk types;
k = 1…nl, nl = the number of the identified loss types.
Phase 2
Risks and losses are categorized into 4 classes in accordance with Boverket (2007).
An index between 1 and 4 is given for each class; the index value 1 expresses the
less damaging situation, while the index value of 4 corresponds to the most dangerous situation.
Phase 3
Each risk type is analyzed from system point of view; a risk source inventory is thus
obtained. An index value (1–4) is assigned to each risk source, for each loss type; a
probability of occurrence is also provided for each risk type. These values may be
obtained via Delphi polls or a combination of analytical methods, previous
knowledge, and/or expert judgment.
The results are written in the matrix form
0
C¼@
c1;1
cnr;1
...
...
...
c1;nl
cnr;nl
1
A
0
1
p1
and P ¼ @ . . . A
pnl
ð6:25Þ
122
6 Consensus-Driven Models for QVA in Transportation Corridors
with:
1 ci;j 4 and
1 pi 4
C is built with the risk types on lines and loss types on columns; subsequently, ci,j
expresses the ‘loss type i caused by risk type j index.’
Phase 4
The loss index is multiplied with the probability index, for each of the risk types.
The multiplication results for each loss type are summed up.
Let Zi, i = 1…nl indicate the sum previously computed:
Zi ¼
nl X
nl X
cij pi ¼ pi
cij
j¼1
ð6:26Þ
j¼1
The maximum value of Zi is given:
Zimax ¼ max cij max pij nl ¼ 4 4 nl
ð6:27Þ
Pl According to Gheorghe and Vamanu (2003), Ic ¼ nj¼1
cij defines the consequence indicator, and Ip ¼ pi corresponds to the risk indicator. Subsequently,
one gets:
Zi
the risk index associated with risk i
Zmax
the maximum risk index of risk i.
i
Risk (threat) profile of a system is built based on the individual values of Zi. The
sum of all the risk indices measures the collective risks the system is prone to.
Phase 5
During this phase, an inventory of the resources related to the risk management is
performed. The risk-management capability is defined for each risk i, which is a
function of two parameters, αi and βi. The following holds:
0 ai 1;
0 bi 1;
ai þ bi 1:
A value ðai þ bi Þ ¼ 1 is equivalent to a totally managed risk (threat). αi
expresses the risk reduction/elimination capability, loss compensation, and consequence mitigation. This is a generic characteristic of a given risk type i—its value
does not take into account the specific system characteristics. In turn, systems
characteristic capabilities that deal with a given risk type i are reflected by βi.
6.2 The Relevance Matrices Method
123
Based on αi and βi, the System Robustness Indicator Relative to Risk i is
introduced:
qi ¼ Zi ðai þ bi Þ
ð6:28Þ
Phase 6
The following system’s characterization indices are introduced, using the equations
and results of the previous phases:
I1 = system’s maximum threat (risk) level
¼ Z max nr
ð6:29Þ
I2 = system’s current risk level
nr
X
ð6:30Þ
Zi
i¼1
I3 = system’s current level of performance in managing
nr
X
ðai þ bi ÞZi
ð6:31Þ
i¼1
Recalling from the previous section that
I2
I1
reflects the relative risk level the
I3
I2
system is exposed to, is the quality of the risk-management (mitigation) capabilities of the system governing entity (local authority, corporate management, etc.),
and that system’s robustness and resilience gets higher as II32 a dynamic variable of
the system gets closer to 1. Current authors introduce the following definition for
vulnerability of a system:
V ¼1
I3
I2
ð6:32Þ
It is easy to see that vulnerability as given as in Eq. (6.32) is computed as
function of system resilience and that V = 0 and V = 1 correspond to completely
vulnerable and non-vulnerable (minimum vulnerability) systems.
6.2.2
Transportation Corridor Vulnerability Assessment
Model with the Relevance Matrices Method
This section covers the proposed model for assessing vulnerability of transportation
corridors, built on top of the matrix method as described above. The model is driven
by the following assumptions and amendments of the generic method:
124
6 Consensus-Driven Models for QVA in Transportation Corridors
• The Transportation Corridor (Segment) is characterized at every point by
temporal, spatial, political, and social features of the vicinity of the transportation segment (near operation environment). These features will be named
location features, characterizing the assessment point.
• The transportation system is defined in every assessment point by (i) the correlation matrix C (risk types versus loss types) and the P vector of the probabilities which holds the probability of occurrence for each of the considered
risks
• The effective values of losses (LTi) due to each type of risks (RTj) are dynamically computed in each assessment point, depending on the location features.
Let us denote:
LTi[RTj] is the effective value of loss i due to risk j.
A = F[B, C, D]—reads A depends on B, C, and D.
• I1, I2, I3 are computed for each assessment point.
• After the completion of previous steps, one gets the Vulnerability Profile and the
overall Vulnerability Index of the transportation system (V).
The model uses the following supplemental variables:
Trep [h/km]—the average time for repairing/building 1 km of rolling infrastructure
(highway, railway—for road and rail transportation, respectively). The value of Trep
depends on Rtt (road, railway, highway).
Crep [EUR/km]—the repair cost for one kilometer of rolling infrastructure;
depending on Rtt.
ρpop [loc/km2]—population density; depending on location (dcity, dtown).
Ccr [EUR/km2]—cleanup and reconstruction costs.
Cpr [EUR/km2]—(private) property cost.
Ndeaths_road [person/accident]—number of fatalities due to road accidents:
Ndeaths
road
¼
Ndeaths;road accidents ½person
Nroad accidents ½accident
Ndeaths_rail [person/accident]—number of fatalities due to rail accidents:
Ndeaths
rail
¼
Ndeaths;rail accidents ½person
Nrail accidents ½accident
Notice that Ndeaths,x is the ratio between the total number of fatalities resulting from
the accidents of type x during one year and the total number of road/rail accidents
that occur in the same year. In some cases, this information is readily available from
different agencies (e.g., Insurance Institute for Highway Safety) at the national and
regional levels.
6.2 The Relevance Matrices Method
125
Nwounded_road [person/accident]—number of the wounded due to road accidents:
Nwounded
road
¼
Nwounded;road accidents ½person
½accident
Nroad accidents
Nwounded_rail [person/accident]—number of the wounded due to rail accidents:
Nwounded
rail
¼
Nwounded;rail accidents ½person
½accident
Nrail accidents
MOD—the transportation type (urban, urban (towns), extraurban).
Sa [km2]—the affected area:
Sa ¼ p R2rel =1;000;000
Laffected [km]—the length of the transportation segment that is affected by a disruptive event:
Laffected ¼
2 Rrel
1000
Rrel_medical—the maximum distance to which a medical center may be located, as to
provide prompt intervention in the case of an accident.
Rrel_interventie—the maximum distance up to which an emergency intervention center
(fire station, etc.) may be located, as to ensure a prompt intervention for mitigating
the effects of a LOC accident.
α[]—mitigating/aggravating factor, probabilities,
β[]—mitigating/aggravating factor, losses.
The model is designed for providing a solution to the following:
The Problem
Organizer: the National Transportation Board.
Assessment goal: ensuring an optimal operability of the National Transportation
System. This is done by:
(i)
(ii)
(iii)
(iv)
estimating maximum risk level induced by the assessed activity;
estimating current risk level on a given transportation segment;
estimating robustness of the transportation system;
performing quantitative assessment of vulnerability of the given transportation
system.
The identification of the risk types relevant to the transportation system—the
indicators selection
We propose the following risk types for the model. Risk types are grouped into
three classes as indicated in Table 6.3.
126
6 Consensus-Driven Models for QVA in Transportation Corridors
Table 6.3 Risk classification by classes
Risk types (sources)
Classes
RT1 accident
RT2 LOC followed by effects
RT3 airports
RT4 ‘sensitive objects’ (HV lines, bridges)
RT5 traffic control and management
RT6 medical personnel intervention delays
RT7 emergency personnel intervention delays (firefighters, civil
protection)
RT8 floods
RT9 snowstorms
RT10 landslides
RT11 avalanches
RT12 forest fire
RT13 earthquake
RT14 safety culture
RT15 terrorism
RT16 insurance system
RT17 legislation
RT18 political stability
Disruptive potential
Disruptive potential
Disruptive potential
Disruptive potential
Infrastructure and services
Infrastructure and services
Infrastructure and services
Disruptive potential
Disruptive potential
Disruptive potential
Disruptive potential
Disruptive potential
Disruptive potential
Operational climate
Operational climate
Operational climate
Operational climate
Operational climate
Identification of potential loss types of a transportation system
The loss types considered within the model are:
LT1
LT2
LT3
LT4
LT5
LT6
LT7
LT8
Traffic on the analyzed segment stopped (hours);
Traffic delayed on the analyzed segment (hours);
Rolling infrastructure repair costs (EUR);
Transportation system remedy costs (EUR);
Property loss (EUR);
Fatalities (persons);
Injuries (persons);
Environmental damages (affected ha);
Loss and probability classification
Corresponding to Phase 2 of the assessment schema, loss and probability classification is left to expert judgment, as a means of reflecting different stakeholder
perspectives.
Filling in the correlation matrices
In current research, authors opt for computing effective values for both, type of loss
and type of risk correlation and probability of occurrence of a given risk type based
on the characteristics of the location.
6.2 The Relevance Matrices Method
127
The following set of equations is suggested for computing the effective values.
The equations are provided as follows: for each risk type, a set of equations is given
in order to compute the effective value of each loss.
RT1 Accident (road, rail)
The model assumes that the probability of occurrence of a disruptive event characterized by RT1 equals the probability of occurrence of an accident computed
using the comprehensive methodology presented in Chap. 3. There is no consideration of any hazmat transportation-related aspects such as lorry/train, load type.
Obtained probability is denoted as P*. P* and is adjusted by aggravating factors
depending on Rtt, Rtq, and MOD.
MOD is taken into account for when including pedestrian-involving accidents,
such as in the case of a city/town transportation segment.
PfRT1 g ¼ F½P ½LOC; Rt1 ; Rtq ; MOD
ð6:33Þ
PfRT1 g ¼ P ½LOC a0 ½Rtt Rtq a00 ½MOD
ð6:34Þ
with α′[Rtt] and α″[MOD]—aggravating factors.
LT1{RT1}—Traffic on the analyzed segment stopped (hours);
LT1 fRT1 g ¼ F½Rtt ð6:35Þ
LT2{RT1}—Traffic delayed on the analyzed segment (hours):
LT2 fRT1 g ¼ F ½LT1 fRT1 g; Rt1 ¼ LT1 fRT1 g b½Rtt ð6:36Þ
LT3{RT1}—Rolling infrastructure repair costs:
LT3 fRT1 g ¼ F½Rtt ð6:37Þ
LT4{RT1}—Transportation system remedy costs:
Only the costs for transportation segment decongestion are considered.
LT4 fRT1 g ¼ F½Rtt ð6:38Þ
LT5{RT1}—Property loss (EUR):
LT5 fRT1 g ¼ F ½A; MOD ¼ A b½MOD
with
A
ð6:39Þ
the average cost of the LORRY/CAR or average cost TRAIN/
LOCOMOTIVE
β[MOD] aggravating factor considering additional losses due to hitting a building.
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6 Consensus-Driven Models for QVA in Transportation Corridors
LT6{RT1}—Fatalities (no. of persons):
LT6 fRT1 g ¼ F Nfatalitites;x ; MOD ¼ Nfatalites;x b½MOD
ð6:40Þ
with
β[MOD] aggravating factor, taking into account the additional number of fatalities
from pedestrians.
LT7{RT1}—Injuries (no. of persons):
LT7 fRT1 g ¼ F Ninjured;x ; MOD ¼ Ninjured;x b½MOD
ð6:41Þ
with
β[MOD] aggravating factor, taking into account the additional number of injured
pedestrians.
LT8{RT1}—Environmental losses
LT8 fRT1 g ¼ 0
ð6:42Þ
RT2 Loss of containment accident followed by effects
The Loss of containment accident followed by effects probability equals the probability of occurrence of an accident computed by using the methodology in
Sect. 3.2.1 where probability of loss of containment is represented by P[LOC]. P
[LOC] is adjusted by aggravating factors depending on the rolling infrastructure
type and quality (Rtt and Rtq) and the transportation type (MOD). MOD is taken
into account because TR2 is assumed as including the pedestrians involving
accidents.
PfRT2 g ¼ F P½LOC; Rtt ; Rtq ; MOD
PfRT2 g ¼ P½LOC a0 ½Rtt Rtq a00 ½MOD
ð6:43Þ
with α′ [Rtt] and α″[MOD] adjustment factors.
Here, α″[MOD] should be selected as to reflect the following interpretation:
• Measurement point inside a city: Transportation system’s vulnerability from the
LOC accident viewpoint is smaller than the one in an extraurban transportation,
due to smaller speeds (a00 is a mitigating factor, a00 \1Þ
• Measurement point inside a town: System’s vulnerability is higher than the
extraurban case, due to not necessarily smaller speeds but an increase of the
number of the potentially accident initiating factors (a00 is an aggravating factor,
a00 [ 1Þ
• Measurement point outside populated places: α″ = 1.
6.2 The Relevance Matrices Method
129
Potential loss is computed in the ‘worst-case scenario.’ Thus, it is assumed that
(i) all possible physical effects are characteristic for the transported substance and
(ii) all the physical effects (fire, explosion, etc.) may follow the loss of containment.
LT1{RT2}
LT1—Traffic on the analyzed segment stopped (hours):
LT1 fRT2 g ¼ F Rtt ; Trep ; Laff ¼ b½Rtt Trep ½Rtt Laff
ð6:44Þ
LT2{RT1}—Traffic delayed on the analyzed segment (hours):
LT2 fRT2 g ¼ F ½LT1 fRT2 g; Rt1 ¼ LT1 fRT2 g b½Rtt ð6:45Þ
with
β[Rtt] aggravating factor.
LT3{RT2}—Rolling infrastructure repair costs:
LT3 fRT2 g ¼ FCrep ; Laff ; Rtt ¼ b½Rtt Crep ½Rtt Laff
ð6:46Þ
TP4{TR2}—Transportation system remedy costs:
This cost includes cleanup and reconstruction costs of the affected area, and
depends on the location of the accident. Consequently,
LT4 fRT2 g ¼ F ½MOD; Saff ¼ Saff Ccr ½MOD
ð6:47Þ
LT5{RT2}—Property loss:
Depends on a number of factors including:
•
•
•
•
•
average price per m2;
affected surface;
distance toward a city;
distance toward a town;
effects adjustment factors.
LT5 fRT2 g ¼ F ½MOD; Saff ¼ Cpr
city
þ Cpr
town
þ Cpr
extraurban
ð6:48Þ
with Cpr_oraş, Cpr_localitate, Cpr_extravilan as contributors to the final cost depending on
the urban development level in the vicinity of the measurement point.
(
Cpr
city
¼
(
Cpr
town
¼
d
0
bcity Saff 1 Rcity
Cpr
rel
0;
0
btown Saff 1 dRtown
Cpr
rel
0;
city ;
town ;
for dcity Rrel
for dcity Rrel
fordtown Rrel
fordtown Rrel
ð6:49Þ
ð6:50Þ
130
6 Consensus-Driven Models for QVA in Transportation Corridors
Cextraurban ¼ bextraurban Saff
ð6:51Þ
with
C′pr_city, C′pr_town, C′pr_extraurban the average costs per 1 km2 property.
LT6{RT2}—Fatalities (no. of persons):
The number of fatalities due to RT2 is assumed as a fraction of the total number
of persons injured in the same circumstances.
LT6 fRT2 g ¼ F ½LT7 fRT2 g; b ¼ b LT7 fRT2 g
ð6:52Þ
LT7{RT2}—Injuries (no. of persons):
LT7 fRT2 g ¼ F Saff ; MOD; qpop ; b ¼ Saff qpop ½MOD b
ð6:53Þ
with
β mitigating factor equal to the percentage of the exposed population injured by
the LOC physical effects
LT8{RT2}—Environmental losses [km2]:
LT8 fRT2 g ¼ Saff ¼
p R2rel
106
ð6:54Þ
RT3 Airports
The presence of airports induces a higher vulnerability to a transportation system.
To avoid double counting, RT3 accounts only for loss contributions resulting from
the presence of an airport.
The probability of occurrence of an event characterized by RT3 is computed
from the probability of occurrence of a LOC accident, adjusted by aggravating
factors depending on the distance to the closest airport (daip) and the number of
airports in the relevance radius (Naip).
PfRT3 g ¼ F P½LOC; daip ; Naip ; Rrel
(
1d
P½LOC Naip Rrelaip ; for daip Rrel
PfRT3 g ¼
0;
for daip [ Rrel
ð6:55Þ
As a result of the introductory remarks, one has:
LT1{RT3}—Traffic on the analyzed segment stopped (hours):
LT1 fRT3 g ¼ 0
ð6:56Þ
6.2 The Relevance Matrices Method
131
LT2{RT3}—Traffic delayed on the analyzed segment (hours):
LT2 fRT3 g ¼ 0
ð6:57Þ
LT3{RT3}—Rolling infrastructure repair costs:
LT3 fRT3 g ¼ 0
ð6:58Þ
LT4{RT3}—Transportation system remedy costs:
LT4 fRT3 g ¼ 0
ð6:59Þ
LT5{RT2} Property loss (EUR):
Is taken as a function of:
•
•
•
•
average price per km2 in the case of an airport;
affected surface;
distance toward an airport;
effects adjustment factors.
LT5 fRT3 g ¼ F daip ; Saff ¼ Cpr
aip
Saff b daip
1
Rrel
ð6:60Þ
with
Cpr_aip average cost of 1 km2 of airport property;
β
effects adjustment factor.
LT6{RT3} Fatalities (no. of persons):
LT6 fRT3 g ¼ 0
ð6:61Þ
LT7{RT3}—Injuries (no. of persons):
LT7 fRT3 g ¼ 0
ð6:62Þ
LT8{RT3}—Environmental losses [km2]:
LT8 fRT3 g ¼ 0
ð6:63Þ
RT4 ‘Sensitive’ objects
Current model considers as ‘sensitive objects’ of infrastructure elements (not necessarily road/rail related) that (i) may increase losses and (ii) increase the probability of occurrence of a LOC accident in their vicinity. For simplicity and reduced
complexity, the model considers bridges and high-voltage lines (HV lines) as
sensitive objects.
132
6 Consensus-Driven Models for QVA in Transportation Corridors
Similar to the case of airports, only the loss contributions resulting from the
presence of ‘sensitive objects’ are taking into account to avoid double counting.
The probability of occurrence of an event characterized by RT4 is defined as the
probability of occurrence of a LOC accident adjusted by aggravating factors
depending on the distance to the closest HV line (dHV) and the distance to the
closest bridge (dbridge).
PfRT4 g ¼ F P½LOC; dHV ; dbridge ; Rrel
PfRT4 g ¼ P½LOC abridge aHV
ð6:64Þ
where αbridge and αHV are given as:
(
abridge ¼
1
dbridge
Rrel
;
for dbridge Rrel
fordbridge [ Rrel
ð6:65Þ
;
fordHV Rrel
fordHV [ Rrel
ð6:66Þ
0;
and
(
aHV ¼
1
dHV
Rrel
0;
LT1{RT4}—Traffic on the analyzed segment stopped (hours);
Depending on the number of bridges (Nbridges) on the assessed segment and the
time the traffic is stopped due to a LOC accident (TP1{TR2}):
LT1 fRT4 g ¼ F LT1 fRT2 g; Nbridges ¼ b Nbridges LT1 fRT2 g
ð6:67Þ
β > 1 (β = 5 recommended value).
LT2{RT4}—Traffic delayed on the analyzed segment (hours):
Given as function of the number of bridges (Nbridges) on the assessed segment
and the time the traffic is delayed due to a LOC accident (TP2{TR2}):
LT2 fRT4 g ¼ F LT2 fRT2 g; Nbridges ¼ b Nbridges LT2 fRT2 g
ð6:68Þ
β > 1.
LT3{RT4}—Rolling infrastructure repair costs:
LT3 fRT4 g ¼ F LT3 fRT2 g; Nbridges ¼ b Nbridges LT3 fRT2 g
ð6:69Þ
β > 1.
LT4{RT4}—Transportation system remedy costs:
LT4 fRT4 g ¼ 0
ð6:70Þ
6.2 The Relevance Matrices Method
133
LT5{RT4}—Property loss (EUR):
Depends on a number of factors including:
•
•
•
•
•
•
the distance to the closest HV line;
the number of HV lines crossed along the segment;
the number of bridges along the segment;
unit average cost of a HV line
unit average cost of a bridge
the adjustment factors function of dHV.
LT5 fRT4 g ¼ F dHV ; dbridge ; Cbridge ; CHV ; Nbridges ; NHV
¼ Cbridge Nbridges þ CHV NHV b½dHV ð6:71Þ
with
β [dHV] mitigation factor,
(
bHV ¼
1
dHV
Rrel
;
0;
for dHV Rrel
for dHV [ Rrel
ð6:72Þ
LT6{RT4}—Fatalities (no. of persons):
LT6 fRT4 g ¼ 0
ð6:73Þ
LT7{RT4}—Injuries (no. of persons):
LT7 fRT4 g ¼ 0
ð6:74Þ
LT8{RT4}—Environmental losses [km2]:
LT8 fRT4 g ¼ 0
ð6:75Þ
TR5 Traffic control and management
TR5 expresses the characteristic risk of a transportation segment induced by the
absence of traffic control and management systems.
The value of the potential losses depending on TR5 is given, in a similar manner
as in the previous cases, as supplemental contributions to losses caused by an LOC
accident. The TR5-specific probability is in direct relation to the presence/absence
of traffic control equipment. Hence, it is assumed that the vulnerability of a
transportation segment is in inverse relationship with the probability of traffic
control systems missing on the analyzed segment.
The probability of occurrence of a disruptive event due to TR5 (PfTR5 g) is
computed by adjusting the LOC probability, with aggravating factors depending on
the transportation type (MOD) and type of the rolling infrastructure Rtt..
134
6 Consensus-Driven Models for QVA in Transportation Corridors
PfTR5 g ¼ F ½P½LOC; MOD; Rt PfTR5 g ¼ P½LOC ða0 ½MOD a00 ½Rt Þ
ð6:76Þ
LT1{RT5}—Traffic on the analyzed segment stopped (hours);
LT1 fRT5 g ¼ 0
ð6:77Þ
LT2{RT1}—Traffic delayed on the analyzed segment (hours):
LT2 fRT5 g ¼ 0
ð6:78Þ
LT3{RT1}—Rolling infrastructure repair costs:
LT3 fRT5 g ¼ 0
ð6:79Þ
LT4{RT1}—Transportation system remedy costs:
LT4 fRT5 g ¼ 0
ð6:80Þ
LT5{RT1}—Property loss (EUR):
LT5 fRT5 g ¼ 0
ð6:81Þ
LT6{RT5}—Fatalities (no. of persons):
Computed as a percent (β) of the total number of fatalities (accidents and LOC
accidents)
LT6 fRT5 g ¼ F ½LT6 fRT1 g; LT6 fRT2 g ¼ b ðLT6 fRT1 g þ LT6 fRT2 gÞ ð6:82Þ
LT7{RT5}—Injuries (no. of persons):
Computed as a percent (β) of the total number of fatalities (accidents and LOC
accidents)
LT7 fRT5 g ¼ F ½LT7 fRT1 g; LT7 fRT2 g ¼ b ðLT7 fRT1 g þ LT7 fRT2 gÞ ð6:83Þ
LT8{RT1}—Environmental losses
LT8 fRT5 g ¼ 0
ð6:84Þ
RT6 Medical personnel intervention delays
It is assumed that the vulnerability of the transportation segment is in direct relationship with the probability of delayed intervention of the medical personnel. The
RT6-associated probability is computed as function of the distance toward the
closest city/town (dcity, dtown).
6.2 The Relevance Matrices Method
135
PfRT6 g ¼ F dcity ; dtownt
(
PfRT6 g ¼
1
minðdcity ;dtown Þ
Rrel
medical
0;
;
for Rrel
for Rrel
ð6:85Þ
min dcity ; dtown
medical [ min dcity ; dtown
medical
LT1{RT6}—Traffic on the analyzed segment stopped (hours);
LT1 fRT6 g ¼ 0
ð6:86Þ
LT2{RT6}—Traffic delayed on the analyzed segment (hours):
LT2 fRT6 g ¼ 0
ð6:87Þ
LT3{RT6}—Rolling infrastructure repair costs:
LT3 fRT6 g ¼ 0
ð6:88Þ
LT4{RT6}—Transportation system remedy costs:
LT4 fRT6 g ¼ 0
ð6:89Þ
LT5{RT6}—Property loss (EUR):
LT5 fRT6 g ¼ 0
ð6:90Þ
LT6{RT6}—Fatalities (no. of persons):
Computed as a percent (β) of the total number of fatalities (accidents and LOC
accidents)
LT6 fRT6 g ¼ F ½LT6 fRT1 g; LT6 fRT2 g ¼ b ðLT6 fRT1 g þ LT6 fRT2 gÞ ð6:91Þ
LT7{RT6}—Injuries (no. of persons):
Computed as percent (β) of the total number of fatalities (accidents and LOC
accidents)
LT7 fRT6 g ¼ F ½LT6 fRT1 g; LT6 fRT2 g ¼ b ðLT6 fRT1 g þ LT6 fRT2 gÞ ð6:92Þ
LT8{RT1}—Environmental losses [km2]:
LT7 fRT6 g ¼ 0
ð6:93Þ
RT7 Emergency personnel intervention delays (firefighters, civil protection)
It is assumed that vulnerability of a transportation segment is in direct relationship
with the probability of delayed intervention of the emergency personnel. It is also
assumed that expert emergency personnel can only be found in cities.
136
6 Consensus-Driven Models for QVA in Transportation Corridors
The probability associated with RT7 is computed as function of the distance
toward the closest city (dcity).
PfRT7 g ¼ F dcity
(
PfRT7 g ¼
1 Rrel
dcity
emmergency
0;
;
ð6:94Þ
for Rrel emergency dcity
Rrel emergency [ dcity
LT1{RT7}—Traffic on the analyzed segment stopped (hours);
LT1 fRT7 g ¼ 0
ð6:95Þ
LT2{RT7}—Traffic delayed on the analyzed segment (hours):
LT2 fRT7 g ¼ 0
ð6:96Þ
LT3{RT7}—Rolling infrastructure repair costs:
LT3 fRT7 g ¼ 0
ð6:97Þ
LT4{RT7}—Transportation system remedy costs:
Computed as a percent of the transportation remedy costs in case of a LOC
accident.
LT4 fRT7 g ¼ F ½LT4 fRT2 g ¼ b ðLT4 fRT2 gÞ
ð6:98Þ
LT5{RT7}—Property loss (EUR):
Computed as a percent of the total property losses:
LT5 fRT7 g ¼ F ½LT5 fRT2 g; LT5 fRT1 g; LT5 fRT4 g
¼ b ðLT5 fRT2 g þ LT5 fRT1 g þ LT5 fRT4 gÞ
ð6:99Þ
LT6{RT7}—Fatalities (no. of persons):
Computed as a percent (β) of the total fatalities (accident and LOC accident).
LT6 fRT7 g ¼ F ½LT6 fRT1 g; LT6 fRT2 g ¼ b ðLT6 fRT1 g þ LT6 fRT2 gÞ
ð6:100Þ
LT7{RT7}—Injuries (no. of persons):
Computed as a percent (β) of the total injuries (accident and LOC accident).
LT7 fRT7 g ¼ F ½LT7 fRT1 g; LT7 fRT2 g ¼ b ðLT7 fRT1 g þ LT7 fRT2 gÞ
ð6:101Þ
6.2 The Relevance Matrices Method
137
LT8{RT7}—Environmental losses
Computed as a percent (β) of the environmental losses in the case of LOC
accident.
LT8 fRT7 g ¼ F ½LT8 fRT2 g ¼ b ðLT8 fRT2 gÞ
ð6:102Þ
RT8 Floods
It is assumed that probability associated with TR8 depends on the distance to the
closest water body (driver, dwb) and the location of the measurement point inside a
potentially floodable area (Flood).
PfRT8 g ¼ F½driver ; dwb ; Flood
ð6:103Þ
8
minðdriver ;dwb Þ ; for R minðd ; d Þ
>
rel
river wb
>
Rrel
<1 and measurement point inside floodable area
PfRT8 g ¼
>
> 0; for measurement point outside floodable area
:
1; for measurement point inside floodable area
LT1{RT8}—Traffic on the analyzed segment stopped (hours)—given by statistics
and/or expert judgment.
LT2{RT8}—Traffic delayed on the analyzed segment (hours)—given by statistics
and/or expert judgment.
LT3{RT8}—Rolling infrastructure repair costs:
Computed as a percent of
• the costs due to accident (with and without LOC);
• the additional costs due to the presence of bridges on the analyzed segment:
LT3 fRT8 g ¼ F ½LT3 fRT1 g; LT3 fRT2 g; LT3 fRT4 g
¼ b ðLT3 fRT1 g þ LT3 fRT2 g þ LT3 fRT4 gÞ
ð6:104Þ
LT4{RT8}—Transportation system remedy costs:
LT4 fRT8 g ¼ 0
ð6:105Þ
LT5{RT8}—Property loss (EUR):
Computed as a percent of
• the costs due to accident (with and without LOC);
• the additional costs due to the presence of sensitive objects on the analyzed
segment:
LT5 fRT8 g ¼ F ½LT5 fRT1 g; LT5 fRT2 g; LT5 fRT4 g
¼ b ðLT5 fRT1 g þ LT5 fRT2 g þ LT5 fRT4 gÞ
ð6:106Þ
138
6 Consensus-Driven Models for QVA in Transportation Corridors
LT6{RT8}—Fatalities (no. of persons):
LT6 fRT8 g ¼ 0
ð6:107Þ
LT7{RT8}—Injuries (no. of persons):
LT7 fRT8 g ¼ 0
ð6:108Þ
LT8{RT1}—Environmental losses [km2]
Computed as a percent of the losses due to LOC accident:
LT8 fRT8 g ¼ F ½LT8 fRT2 g ¼ b ðLT8 fRT2 gÞ
ð6:109Þ
RT9 Snowstorms
The probability associated with RT9 is computed as function of terrain elevation
at the measurement point (hmp) with the assumption that storms/blizzards can only
occur at an elevation between zero level (sea level) and Hmax above the sea level.
PfRT9 g ¼ F hmp
PfRT9 g ¼
ð6:110Þ
h
mp
; for 0 hmp \Hmax
1 Hmax
0;
otherwise
LT1{RT9}—Traffic on the analyzed segment stopped (hours);
Computed as a percent (β) of the time the traffic is stopped on the analyzed
segment due to accidents (with and without LOC)
LT1 fRT9 g ¼ F ½LT1 fRT1 g; LT1 fRT2 g
¼ b ðLT1 fRT1 g þ LT1 fRT2 gÞ
ð6:111Þ
LT2{RT9}—Traffic delayed on the analyzed segment (hours):
LT2 fRT9 g ¼ F ½LT2 fRT1 g; LT2 fRT2 g
¼ b ðLT2 fRT1 g þ LT2 fRT2 gÞ
ð6:112Þ
LT3{RT9}—Rolling infrastructure repair costs:
LT3 fRT9 g ¼ 0
ð6:113Þ
LT4{RT9}—Transportation system remedy costs:
LT4 fRT9 g ¼ 0
ð6:114Þ
6.2 The Relevance Matrices Method
139
LT5{RT9}—Property loss (EUR):
Computed as a percent (β) of the property losses following a LOC accident in the
case of a delayed intervention of the emergency team.
LT5 fRT9 g ¼ F ½LT5 fRT2 g ¼ b ðLT5 fRT2 gÞ
ð6:115Þ
LT6{RT9}—Fatalities (no. of persons):
Computed as the number of fatalities due to delayed intervention of the medical
and emergency teams, multiplied by the aggravating factor (β).
LT6 fRT9 g ¼ F ½LT6 fRT6 g; LT6 fRT7 g ¼ b ðLT6 fRT6 g þ LT6 fRT7 gÞ
ð6:116Þ
LT7{RT9}—Injuries (no. of persons):
Computed in the same assumptions as LT6:
LT7 fRT9 g ¼ F ½LT7 fRT6 g; LT7 fRT7 g ¼ b ðLT7 fRT6 g þ LT7 fRT7 gÞ
ð6:117Þ
LT8{RT9}—Environmental losses [km2]
LT8 fRT9 g ¼ 0
ð6:118Þ
RT10 Landslides
The probability associated with RT9 is computed as function of terrain elevation
at the measurement point (hmp) with the assumption that landslides can only occur
at an elevation within Hmin and Hmax above the sea level (hilly site).
PfRT10 g ¼ F hmp
(
PfRT9 g ¼
1;
for Hmin hmp \Hmax
0;
otherwise
ð6:119Þ
LT1{RT10}—Traffic on the analyzed segment stopped (hours);
Computed as a percent (β) of the time the traffic is stopped on the analyzed
segment due to accidents (with and without LOC)
LT1 fRT10 g ¼ F ½LT1 fRT1 g; LT1 fRT2 g
¼ b ðLT1 fRT1 g þ LT1 fRT2 gÞ
ð6:120Þ
140
6 Consensus-Driven Models for QVA in Transportation Corridors
LT2{RT10}—Traffic delayed on the analyzed segment (hours):
LT2 fRT10 g ¼ F ½LT2 fRT1 g; LT2 fRT2 g
¼ b ðLT2 fRT1 g þ LT2 fRT2 gÞ
ð6:121Þ
LT3{RT10}—Rolling infrastructure repair costs:
LT3 fRT10 g ¼ F ½LT3 fRT1 g; LT3 fRT2 g
¼ b ðLT3 fRT1 g þ LT3 fRT2 gÞ
ð6:122Þ
LT4{RT10}—Transportation system remedy costs:
LT4 fRT10 g ¼ F ½LT4 fRT1 g; LT4 fRT2 g
¼ b ðLT4 fRT1 g þ LT4 fRT2 gÞ
ð6:123Þ
LT5{RT10}—Property loss (EUR):
Computed as a percent (β) of the losses following a LOC accident:
LT5 fRT10 g ¼ F ½LT10 fRT2 g ¼ b LT10 fRT2 g
ð6:124Þ
LT6{RT10}—Fatalities (no. of persons):
Computed as the number of fatalities due to delayed intervention of the medical
and emergency teams, multiplied by the aggravating factor (β).
LT6 fRT10 g ¼ F ½LT6 fRT6 g; LT6 fRT7 g ¼ b ðLT6 fRT6 g þ LT6 fRT7 gÞ
ð6:125Þ
LT7{RT10}—Injuries (no. of persons):
Computed in the same assumptions as LT7:
LT7 fRT10 g ¼ F ½LT7 fRT6 g; LT7 fRT7 g ¼ b ðLT7 fRT6 g þ LT7 fRT7 gÞ
ð6:126Þ
LT8{RT10}—Environmental losses
Computed as a percent (β) of the environmental losses following a LOC
accident:
LT8 fRT10 g ¼ F ½LT8 fRT2 g ¼ b LT8 fRT2 g
ð6:127Þ
The effective values (LTi) in the case of RT11–RT18 are computed similar to
RT10. This is done by adjusting the already-computed values of losses with
mitigating/aggravating factors (β). Assumptions at the base of computing the RT11–
RT18 are associated with probabilities and are given as:
6.2 The Relevance Matrices Method
141
• P[RT11] is computed based on the assumption that there are no avalanches
below 1000 m elevation.
• P[RT12] depends on a measurement point being in a forest area.
• P[TR13] is computed as a function related to proximity to seismic characteristics
of the measurement point:
P½RT13 ¼
Earthquake
10
ð6:128Þ
with 0 Earthquake\10 (according to the Modified Mercalli Intensity Scale)
• P[TR14], P[TR18] are assumed as being given by expert judgment.
The functional logic of the model is given in Fig. 6.4. Notice that the white
spaces correspond to LTi RTj ¼ 0.
Now, the relevance matrices model may be applied to the filled-in correlation
matrices. For simplicity, it is assumed that the inventory of the resources allocated
to the system management remains constant throughout the evaluation. According
to the generic model, one is able to get the following elements for each measurement point:
•
•
•
•
•
•
Current risk level of a given system;
Maximum risk level of a given system;
Risk profile of the system as indicated in Fig. 6.5;
Current level of competence in risk management;
Robustness Index;
Vulnerability of the system.
Fig. 6.4 Relationship between the different types of risks and losses
142
6 Consensus-Driven Models for QVA in Transportation Corridors
Fig. 6.5 An example of a
risk profile (risk and
associated resilience index)
Vulnerability profile of an analyzed transportation segment is obtained by
repeating the aforementioned procedure (Eqs. 6.33–6.128) and centralizing the
results. The Vulnerability Index (total vulnerability) of the transportation system is
given by:
mp
1 X
Vi
Nmp i¼1
N
V¼
ð6:129Þ
With
Nmp the number of measurement points;
Vi
system’s vulnerability at measurement point i.
References
Barjonet, P. (2001). Traffic psychology today. Norwell, MA: Kluwer Academic Publishers.
Boverket. (2007). Bostadspolitiken: Svensk politik för boende, planering och byggande under 130
år. 1. uppl. Karlskrona, Sweden: Boverket.
Ciscar, J. C., Russ, P., Parousos, L., & Stroblos, N. (2004). Vulnerability of the EU economy to oil
shocks: A general equilibrium analysis with the GEM-E3 Model. Presented at the 13th Annual
Conference of the European Association of Environmental and Resource Economics,
Budapest, Hungary. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.
196.3905
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143
Clemson, B. (1984). Cybernetics: A new management tool. Tunbridge Wells, Kent, UK: Abacus
Press.
Gheorghe, A. V., & Vamanu, D. V. (2003). AIDRAM—Aiding Risk Assessment and Management:
Concept proof software developed by appointment of the Disaster Risk Management Institute,
World Bank. Washington, DC: KOVERS-KT/LSA/ETH Zurich.
Hester, P. T., & Adams, K. M. (2014). Systemic thinking: Fundamentals for understanding
problems and messes. New York, NY: Springer, Berlin Heidelberg.
Kerr, M. (2001). The Delphi Process. In The Delphi pProcess 2002 city: Remote and rural areas
research initiative, NHS in Scotland. Retrieved from http://www.rararibids.org.uk/documents/
bid79-delphi.htm
Nilsson, J., Magnusson, S., Hallin, P., & Lenntorp, B. (2001). Models for vulnerability auditing
and distribution of governmental economical means at the local authority level. Lund, Sweden:
Lund University Centre for Risk Analysis and Management (LUCRAM).
Vamanu, B. I. (2006). Managementul riscurilor privind transportul substanţelor periculoase:
aplicaţii ale sistemelor dinamice complexe (Dissertation, Universitatea Politehnica Bucureşti,
Facultatea de Chimie Aplicată şi Ştiinţa Materialelor, Catedra de Inginerie Economică,
Bucureşti).
Chapter 7
Physical Analogies-Based Model
for Quantitative Vulnerability Assessment
of Transportation Corridors
Abstract This chapter highlights the method for quantitative vulnerability
assessment in multicomponent systems. First, foundational information regarding
multicomponents systems (i.e., assumptions, parameters, vulnerability scale) is
reviewed. It is then shown how the model can be adapted for vulnerability
assessment in transportation corridors.
7.1
Quantitative Vulnerability Assessment Method;
Modeling Cooperative Phenomena
in Multi-component Systems
In the proposed method, adapted from generic Quantitative Vulnerability
Assessment (QVA) model presented in Gheorghe and Vamanu (2004a, b), quantification of vulnerability for a multicomponent system is quantified as follows:
• a two-parameter description of the system and the respective state equation
which includes inputs and outputs. Input includes an arbitrarily large number of
indicators accounting for the system internal process (fast-varying) as well as
external forces (slow-varying) acting upon the system of interest. Output is a
membership fraction indicating integrity of the system in terms of operability
which is defined in terms of proportion of ‘operable’ and ‘inoperable’ states of
the system;
• a division of the two-parameter phase space of the system into vulnerability
basins, including:
– a system stable—low vulnerability,
– a system and vulnerability critical, and
– a system unstable—high vulnerability, regions; and
• a 0–100 Vulnerability Scale and the means to measure the respective
Vulnerability Index, as an operational expression of a QVA.
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_7
145
146
7 Physical Analogies-Based Model for Quantitative Vulnerability …
The generic model addresses cooperative behavior occurring in systems characterized by large number of binary state components (e.g., operational/
dysfunctional, normal/abnormal, and positive/negative). These multicomponent
systems are traditionally the subject of statistical physics as addressed, for example,
in the Ising and Heisenberg models (Vamanu et al. 2003). The relevance of Ising
and Heisenberg models to vulnerability comes from the phenomenology of multicomponent systems. Multicomponent binary systems present state coalitions (i.e.,
‘domains’ in magnetism theory) and the possibility of collective disruptive phase
transitions from one state to the other which, in this context, allows expressing the
vulnerability as system’s quantifiable propensity of suffering such transitions.
The described physical analogies allow for defining individual binary transition
probabilities (i.e., Bragg–Williams approximation, Bragg and Williams 1934) as a
function of two ‘energy’-wise parameters—one characterizing the internal interactions (‘exchange’) and the other the external influence (‘field’). Furthermore,
current extension of this model allows expressing the two parameters as fuzzy
impact functions which depends on an arbitrary number of macroscopic indicators.
Indicators serve a twofold purpose of reflecting a link to the physical reality and
accounting for stakeholder subjectivity.
The assumption of the large number of components allows the interpretation of
the membership fraction (i.e., ratio between the functional and dysfunctional elements of the system) as continuous variable. This enables the development of an
analytical model for describing its dynamics based on a master equation for the
function of distribution of the system states. The master equation encompasses
individual transition probabilities, hence macroscopic indicators of a system.
The same assumption validates the approximation of the master equation by a
series expansion to the 2nd order of the state distribution function (i.e., ratio of
membership fraction and total number of components). The result is a Fokker–
Planck-type equation (Risken 1996). Looking for the stationary solution of this
equation and approximating the result to the 2nd order, one gets the system’s state
equation—in fact, this is a transcendent equation for the extremal surface (i.e., the
surface of the maximum probability) on which the system states may localize.
The state equation defines a topological cusp foil in a 3D-space generated by
exchange parameter (U), field parameter (V), and membership fraction itself. The
foil projection on the [U, V] plane marks a cusp frontier that splits the plane in state
basins. Any set of values macroscopic indicators may have at a given time,
determines a unique pair of coordinates in the [U, V] plane (i.e., identifiable state
point), entailing that the system’s dynamics in time is characterized by the trajectory of the state point in the exchange and field parameters in the defined plane.
Figure 7.1 is drawn to represent the UV plane.
Since traversing the cusp line implies collective, massive transitions of the system
components from the functional/productive/normal state to the dysfunctional/
counterproductive/abnormal state, these events can be rendered as ‘catastrophic’ as
in the sense of Catastrophy Theory (Thom 1975). Additionally, the generic QVA
model proposes the use euclidian distance from the current system state to the cusp
line as a means for quantifying the system vulnerability—as propensity of
7.1 Quantitative Vulnerability Assessment Method …
147
Fig. 7.1 A ‘graphical’ sketch of the cooperative phenomena in multi-component, binary systems
experiencing disruptive state transitions. Moreover, proper scaling allows for defining
a metrics for vulnerability of system of interest on a scale of 0–100 with 0 being
minimum vulnerability.
7.1.1
System Description by Indicators
In the QVA approach, vulnerability of a system is interpreted as the system’s virtual
tendency of losing its design functions and/or structural integrity and/or identity
(i.e., the design role) due to two types of influencing factors (i.e., risk characterizing and risk mitigating (management) capability characterizing factors).
Following Vamanu et al. (2003), we denote:
U the risk characterizing factors set;
V the risk mitigating capability factors set;
It is also assumed that all factors are quantifiable and suitable for being expressed
by indicators. Risks that a system (e.g., transportation) is exposed to and identified
by considering the different disruptive states the system may encounter are characterized by the U factors. Consequently, the associated indicators target internal
characteristics of the system and/or reflect the processes that occur within the
system as well as the performance of the system.
The V factors characterize the capability of response/reaction of the system
management to the internal evolutions of the system. In a broader sense, the
V factors characterize the operational environment of the system and the different
influences that may affect system operations. Thus, the associated indicators have to
be external in nature.
The selection of the characteristic indicators is made under the following considerations: (i) indicators should take into account the analytical models for risk
148
7 Physical Analogies-Based Model for Quantitative Vulnerability …
assessment for hazmat transportation and (ii) indicators should reflect the various
characteristics such as temporal, meteorological, spatial that may affect behaviors of
the traffic participants, as well as the impact of traffic on population (and property)
within the vicinity.
7.1.2
The Control Variables
The quantifiable/monitored indicators that contribute to U and V (Xui and Xvj) are
aggregated resulting into two control variables referred to as U and V. Let U be:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p
p
p
p
UðXu1 ; Xu2 ; . . .; Xun Þ ¼ min 1; Xu1
þ Xu2
þ . . . þ Xun
ð7:1Þ
with
Xui ; i ¼ 1; 2; . . .; n the normalized indicators, computed from the physical
indicators (Yui) as:
Xui ¼ Alog10 ðYui Þ þ B;
i ¼ 1; 2; . . .; n
ð7:2Þ
A and B (constants) are, in turn, computed based on two equivalent pairs (asð1Þ
ð1Þ
ð2Þ
ð2Þ
ð1Þ
ð2Þ
sumed as known) ðXi ; Yi Þ and ðXi ; Yi Þ, in which Xi ¼ 0:2 and Xi ¼ 0:6
as suggested by Gheorghe and Vamanu (2004b).
The control variable V is computed in a similar manner:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p
p
p
p
VðXv1 ; Xv2 ; . . .; Xvn Þ ¼ min 1; Xv1
þ Xv2
þ . . . þ Xvm
ð7:3Þ
with
Xvi ; i ¼ 1; 2; . . .; m the normalized indicators, computed from the physical
indicators (Yvi) as:
Xvi ¼ Alog10 ðYvi Þ þ B;
7.1.3
i ¼ 1; 2; . . .; m
ð7:4Þ
System Constituents—System State Space
The previously obtained U and V variables are the control variables of the two-state
multicomponent system. The behavior of such a system is a textbook matter in
statistical physics, where the archetype is known as the Ising Model, which covers
topics of macroscopic properties, stability issues, and phase transitions in multicomponent systems including ferromagnetism, binary alloys, and other order–disorder phenomena (Huang 1963). And although there is not an exact solution, there
7.1 Quantitative Vulnerability Assessment Method …
149
exists a variety of approximations including Bethe–Peierls solution, Bragg–
Williams solution, and the Onsager solution (Gheorghe and Vamanu 2011).
The solution adopted in the generic QVA for modeling vulnerability comes close
to the Bragg–Williams approximation. In this approximation, the membership
fractions in a two-state system can be obtained on certain assumptions for the
probabilities of individual transitions between the two states (functional/
dis-functional). The interplay of the actual, ‘physical’, and potentially numerous
system indicators will result in variations of the aggregated (fuzzy) parameters
[U and V] which in turn will drive the system ‘state’ in and out of a region of
instability.
In a conventional sense, an operable system may thereby appear as:
• Stable and thereby featuring a low vulnerability;
• Critically unstable/vulnerable; or
• Unstable and thereby featuring a high vulnerability.
Beyond these regions, a system may only be found in inoperable. In the current
endeavor, there is assumption that a ‘hazmat transportation’ system is made of
different members or ‘atoms’ such as vehicles and drivers, people interacting with
the transportation segment (permanent or in transit), traffic supportive infrastructure
components such as fuel stations and service stations, traffic control and management system components such as fixed-traffic lights and surveillance cameras, and
mobile–police squads and helicopter surveillance. Members of the system might
also include relevant ‘special/sensitive objectives’ such as hospitals, police headquarters, and emergency unit headquarters and relevant official/administrative
buildings as well as any other entity (animated or otherwise) that can be
accommodated in a sound and defendable manner into a vision of a mutual
interaction and cooperative behavior. This is meant to account for interdependency
associated with mutual influences among different complex systems through which
state of a system influences, and is influenced by, the state of other interconnected
systems (Katina et al. 2014; Keating et al. 2014). This holistic approach of the
QVA model requires that we get a solid metal picture of the aforementioned.
The remainder of this is designed for this purpose. Additional information is provided in Appendix D.
As mentioned before, a ‘member’ of the system may find itself in only two
states: functional or dysfunctional. Assuming that at any given moment t, the
system is characterized by M1 components in the functional state and M2 components in the dysfunctional state. Should M be the total number of the system
components, then one gets:
M1 þ M2 ¼ M
ð7:5Þ
The overall state of the system may then be described via the pair of numbers
(M1, M2). The system dynamics, or ‘motion’ in its state space, will follow from
variations in M1 and M2 that should be consistent with Eq. (7.5).
150
7 Physical Analogies-Based Model for Quantitative Vulnerability …
Smallest transitions in the state of the system would obviously involve alterations by one unit in numbers of members of overall system:
ðM1 1; M2 þ 1Þ
w12
w21 !
ðM1 ; M2 Þ
ðM1 þ 1; M2 1Þ
w12
w21 !
ð7:6Þ
The system is thus both described by the U and V parameters and by a membership fraction ς, defined as:
1¼
M1 M2
2M
ð7:7Þ
Essentially, ς expresses the degree to which the population of components in
state 1 dominates the population of components in state 2. In other words, ς
communicates the overall operability state of the system.
There is an assumption that transitions are governed by the probabilities w12 and
w21 as suggested by Bragg and Williams (1934):
w12 ð1Þ ¼ wM1 e
U1 þ V
H
w21 ð1Þ ¼ wM2 e
U1 þ V
H
ð7:8Þ
ð7:9Þ
Equations [7.8] and [7.9] reflect the cooperative nature of transitions; indeed, the
transition probabilities get higher as their target-state population (number of
members in the target state) is higher. Notice to that although the transition probability w12 from state 1 ‘functional’ to state 2 ‘dysfunctional’ increases following a
linear law with respect to the M1—a natural assumption, it actually decreases
following exponential law with the fraction of population in state 1. Under these
circumstances, the global asymptotic effect is a decrease, faster than linear, of w12
with the population in state 1 for adequate values of the model parameter Θ—which,
due to the conservation of the total number of the system components (M), leads to
an accelerated increase with the population of the target state 2.
This rationale further consolidates the physical analogy with multicomponent,
cooperative systems, by giving to Θ the meaning of a variable proportional with a
sui generis temperature of the system. The tendency of this kind of systems to form,
due to cooperative behavior, ‘domains’ as in ferromagnetism theory or ‘coalitions,’
as in a sociological driven language, is well known. Inside these coalitions, system
members share the same state. Highly relevant to the suggested model are the
following statements:
• at low ‘temperatures’, the domain structure (ordered, having a ‘functional’
dominance) is wide and resilient to the external influences;
• over a ‘critical’ temperature, the domain structure (ordered and functional)
disappears. In this case, the system presents comparable or theoretically equal
shares of ‘functional’ and ‘dysfunctional’ population; no spatial association is
distinguishable;
7.1 Quantitative Vulnerability Assessment Method …
151
• under external influences (V), the system may abruptly and massively (involving
a large number of population members) switch from ‘functional’ to ‘dysfunctional’. The same phenomena occur when internal interactions among members
(U) get higher than a threshold value which depends on V.
Therefore, the state of the system can be described by the probability density
f(U, V, ς). The bounding surface of the probability density in the U, V, ς–space is
given by:
U 1þV
th
¼21
H
ð7:10Þ
with
th the hyperbolic tangent;
Θ Temperature of the system, defined as
Θ = kB * T
where
kB 1/273.15 = sui generis ‘Boltzmann constant’, and
T the sui generis absolute temperature;
Equation (7.10) defines the system state space as a cuspidal foil in U, V, ζ. This
space topology varies with Θ. Space topologies for T = 1 K, T = 273.15 K and
T = 1000 K are given in Fig. 7.1. The images in Fig. 7.2 are generated with the
AIDRAM software as described in the Quantitative Vulnerability Assessment
module (Gheorghe and Vamanu 2003).
Taking the process described by Eq. (7.6), we can write the following rate
(balance, master) equation for the function of distribution f(M1, M2) as:
@f ðM1 ; M2 Þ
¼ w21 ðM1 1; M2 þ 1Þ f ðM1 1; M2 þ 1Þ
@t
þ w12 ðM1 þ 1; M2 1Þ f ðM1 þ 1; M2 1Þ
ðw21 ðM1 ; M2 Þ þ w12 ðM1 ; M2 ÞÞ f ðM1 ; M2 Þ
Then, the membership fraction is defined as:
1¼
M1 M2
2M
So that
1¼
1
for all 1
2;
12 ; for all 2
152
7 Physical Analogies-Based Model for Quantitative Vulnerability …
Fig. 7.2 QVA model representing system phase space configurations on various T
The equivalences are
1
M
1
ðM1 þ 1; M2 1Þ $ 1 þ
M
ðM1 1; M2 þ 1Þ $ 1 and
7.1 Quantitative Vulnerability Assessment Method …
153
This allows rewriting the master equation as:
@f ð1Þ
1
1
1
1
¼ w21 1 f 1
þ w12 1 þ
f 1þ
@t
M
M
M
M
ðw21 ð1Þ þ w12 ð1Þ f ð1ÞÞ
Next,
(a) The assumption that the number M of system agents is large allows a series
expansion of all quantities in the 2nd member of the master equation.
Restricting the expansion to the 2nd order in (1/M), one obtains a continuity
(conservation) equation for the state distribution function f, involving the
‘current’ variable J:
@f
@J
þ
¼ 0;
@t
@1
with J as:
J¼
1
1 @ðw21 þ w12 Þf
ðw21 w12 Þf M
2M 2
@1
(b) Looking for explicitly time independent and stationary solutions of the
aforementioned equation, one gets f as:
"
N exp 2M
f ðfÞ ¼
R1
1=2
#
w21 ðnÞw12 ðnÞ
w21 ðnÞ þ w12 ðnÞ dn
w21 ð1Þ þ w12 ð1Þ
with N being a normalizing constant.
(c) The next step is to look for the extremal surface of the probability density of
@f
states (f), by making @f
equal to zero. After a second series expansion of the
result and again after restricting the series to the 2nd order of (1/M), one gets
the system’s state equation as:
UðfÞ þ V
th
¼ 2f
h
ð7:11Þ
Recall that the state equation defines the U, V, ζ–space of the most probable
states of the system (Ursu et al. 1985).
7 Physical Analogies-Based Model for Quantitative Vulnerability …
154
7.1.4
Vulnerability Basins—The Instability Region
Certainly, a transportation system may find itself (depending on U and V) inside or
outside of one of the instability regions. Thus, it could be said that a functional/
operable system may be:
• Stable, corresponding to a low vulnerability;
• Critically Unstable corresponding to a medium vulnerability, or
• Unstable corresponding to a high vulnerability.
Outside these regions, a system is considered to be inoperable. The instability
regions are delimited in the system state space as in Fig. 7.3.
The instability regions are defined in relation with the cusp line. Again, the cusp
line separates the system state space in areas characterized by:
• a single, real solution ζ of Eq. (7.10);
• two or three real solutions ζ of Eq. (7.10).
Therefore,
• The high vulnerability area (i.e., unstable system) is a section in which
Eq. (7.10) presents two or more solutions.
Fig. 7.3 System instability regions
7.1 Quantitative Vulnerability Assessment Method …
155
• The moderate vulnerability area (i.e., critically unstable system) is a section in
which Eq. (7.10) has a single, positive solution. However, this is located at close
distance to the cusp line.
• The low vulnerability area (i.e., stable system) is a section in which Eq. (7.10)
has a single, positive solution.
Since there is no an exact analytical solution, the equation of the cusp line must
be obtained through an iterative process of identifying a set of points in the system
space (Gheorghe and Vamanu 2003). This follows that for each U > 0, one chooses
Vc as the arithmetic mean between the last V for which system state equation has
three solutions and the first V for which the same equation has only one positive
solution.
7.1.5
The Quantitative Vulnerability Assessment
In consideration of the above, a 0–100 ‘Vulnerability Scale’ and a Vulnerability
Index may be defined based on the assessment of the system state in the (U, V)space. Hence,
(a) The Vulnerability Index is given by the euclidian distance of the state (U, V) to
the cusp line in the U 0; V 0 region of the (U, V)-plane.
(b) The Vulnerability Index is normalized such that, everywhere on the cusp line,
including its U 0; V 0 section, the Vulnerability Index is equal to 100 (i.e.,
reach its assumed maximum).
(c) The Vulnerability Index is assumed to be 100 within the whole region defined
by the cusp line and the U axis of the first (upper-right) quadrant of the system
space.
Consequently, Vulnerability Index is defined as:
1D
Vi ¼ 100 15
with
Vi the vulnerability index,
D the euclidian distance between system’s state and the cusp line
Notice that Eq. (7.12) implies a limitation of U and V as:
0 U 15
0 V 15
ð7:12Þ
7 Physical Analogies-Based Model for Quantitative Vulnerability …
156
The region characterized by a single and positive solution of the state Eq. (7.10)
is considered as the stability region of the system. On the other hand, the region
characterized by three real solutions is the instability region.
The Vulnerability Index equals 100 in the instability region and decreases as the
system gets further away of the cusp line.
7.2
Applying QVA Model for the Vulnerability
Assessment of Transportation Corridors
This section provides details on adaption of the generic QVA model for vulnerability assessment of transportation corridors.
7.2.1
Indicators Selection
Indicators that describe the transportation system have been selected according to
general assumptions articulated in the Sect. 7.1 above. In addition, system vulnerability may be in a direct or inverse relationship with indicator value. This is
based on the indicator meaning (i.e., what the indicator expresses).
Tables 7.1 and 7.2 provide a set of
indicators putforward for
characterizing
the
ð1Þ
ð1Þ
ð2Þ
ð2Þ
ð1Þ
ð1Þ
transportation system. Equivalent pairs XUi ; YUi XUi ; YUi and XVj ; YVj ð2Þ
ð2Þ
XVj ; YVj , assumed a priori known, should be provided by the analyst in the
pre-assessment phase.
7.2.2
Computing the Physical Indicators—YUi and YVj
Relevant physical indicators of the transportation system (external and internal) are
provided in Tables 7.3 and 7.4.
7.2.3
Transportation System Vulnerability Assessment
The vulnerability assessment of a transportation segment may be sketched out as
follows:
• get the physical indicators in every measurement point along a given transportation segment;
• normalized indicators are computed according to Eqs. (7.1 and 7.3);
7.2 Applying QVA Model for the Vulnerability Assessment …
157
Table 7.1 A set of internal (fast varying) indicators
Internal indicators (U-contributors)
Vulnerability–indicator
relationship
XU1. Closest city
XU2. Closest town
XU3. Vegetation in measurement point
XU4. Closest river
XU5. Number of bridges on the current analyzed segment
XU6. Closest in-land water body(including large rivers)
XU7. Number of bridges over the in-land water bodies on the
current segment
XU8. Measurement point in a flooding-prone area
XU9. Rolling infrastructure type
XU10. Quality of the infrastructure type
XU11. Closest airport
XU12. Number of HV lines crossing the current analyzed segment
XU13. Stress level of the traffic participant
Inverse
Inverse
Direct
Inverse
Direct
Inverse
Direct
Direct
Direct
Direct
Inverse
Direct
Direct
Table 7.2 A set of external (slow varying) indicators
External Indicators (V-contributors)
Vulnerability–Indicator Relationship
XV1. Number of rivers within the relevance radius
XV2. Number of cities in the relevance radius
XV3. Number of towns in the relevance radius
XV4. Number of rivers within the relevance radius
XV5. Number of HV lines within the relevance radius
XV6. Number of airports within the relevance radius
XV7. Traffic fluency
XV8. Earthquake danger level
XV9. Measurement point elevation
XV10. Traffic jam propensity on the current segment
Direct
Direct
Direct
Direct
Direct
Direct
Direct
Direct
Direct
Direct
• system control parameters (U and V) are computed following Eq. (7.4);
• compute transportation system vulnerability in the measurement point following
Eq. (7.10).
Processing all the measurement points according the aforementioned algorithms
allows one to get the Vulnerability Profile of a given transportation segment
together with a value of the Vulnerability Index as:
PNmp
Vsegment ¼
i¼1
Nmp
Vi
ð7:13Þ
158
7 Physical Analogies-Based Model for Quantitative Vulnerability …
Table 7.3 A set of External (slow varying) indicators with computational means
Internal Indicators (U-contributors)
Computational means (unit)
YU1. Closest city
YU2. Closest town
YU3. Vegetation in measurement point
Effective distance (m)
Effective distance (m)
Discrete values depending on the vegetation type
(non-dimensional)
Effective distance (m)
Number of intersections between the analyzed
traffic segment and rivers (non-dimensional)
Effective distance (m)
YU4. Closest river
YU5. Number of bridges on the current
analyzed segment
YU6. Closest in-land water body(including
large rivers)
YU7. Number of bridges over the in-land
water bodies on the current segment
YU8. Measurement point in a
flooding-prone area
YU9. Rolling infrastructure type
YU10. Quality of the infrastructure type
YU11. Closest airport
YU12. Number of HV lines crossing the
current analyzed segment
YU13. Stress level of the traffic participant
Number of intersections between the analyzed
traffic segment and in-land waters
(non-dimensional)
Discrete values (non-dimensional)
{0; 1}
Discrete values depending on the rolling
infrastructure type (non-dimensional)
Discrete values (non-dimensional)
{0; 1; 2; 3; 4; 5}
Effective distance (m)
Number of intersections between the analyzed
traffic segment and the HV lines
(non-dimensional)
YU13 ¼ YU10 2þ YU9 (non-dimensional)
Table 7.4 A set of external (slow varying) indicators with computational means
External Indicators (V-contributors)
Computational means (unit)
YV1. Number of rivers within the
relevance radius
YV2. Number of cities in the
relevance radius
YV3. Number of towns in the
relevance radius
YV4. Number of rivers within the
relevance radius
YV5. Number of HV lines within the
relevance radius
YV6. Number of airports within the
relevance radius
YV7. Traffic fluency
YV8. Earthquake danger level
YV9. Measurement point elevation
YV10. Traffic jam propensity on the
current segment
Effective number (non-dimensional)
Effective number (non-dimensional)
Effective number (non-dimensional)
Effective number (non-dimensional)
Effective number (non-dimensional)
Effective number (non-dimensional)
Number of vehicles/km (vehicle/km)
Effective number (non-dimensional)
Elevation to sea-level (m)
Discrete values depending on the rolling infrastructure
type (non-dimensional)
7.2 Applying QVA Model for the Vulnerability Assessment …
159
with
Nmp the number of measurement points;
Vi
system’s vulnerability at measurement point i.
Recall, it is assumed that the transportation corridor contains one or more
transportation routes which, in turn, contains one or more transportation segments.
Consequently, the vulnerability for each of the transportation routes constituent
transportation corridor and is computed as:
PNns
Vroute ¼
j¼1
Vsegment
Nns
j
ð7:14Þ
with
Nns
the number of segments of the route;
Vsegment_j vulnerability index of segment j
and the vulnerability of the transportation corridor is given as:
PNsroutes
Vcorridor ¼
Vroute
Nroutes
l¼1
1
ð7:15Þ
with
Nroutes the total number of routes part of the transportation corridor (system);
Vroute_l vulnerability index of route l,
Summarizing, the ‘Assumption Zero’ of this model is that:
critical, or otherwise complex real-life structures can be accommodated within the concept
of a multi-component, multi-indicator system, the parts of which would show some kind of
collective behavior by virtue of their interactions, as well as some susceptibility to external
factors acting upon parts of the structure.
To quantify vulnerability, for a multicomponent system, a generic model is
proposed. This model provides:
(a) a two-parameter description of the system and the respective equation of state,
having an input of arbitrarily large number of indicators that account for
internal (fast-varying) processes and external (slow-varying) forces acting
upon the system and output of membership fraction indicating the proportion
of system state of ‘operable’ and ‘inoperable’;
7 Physical Analogies-Based Model for Quantitative Vulnerability …
160
(b) a division of the two-parameter phase space of the system into vulnerability
basins, including:
a. a system stable—low vulnerability,
b. a system and vulnerability critical, and
c. a system unstable—high vulnerability, regions; and
(c) a 0–100 Vulnerability Scale and the means to measure the respective
Vulnerability Index as an operational expression of a QVA.
The operative value of the QVA generic model has been tested on a variety of
systems, ranging from nuclear reactors to IT systems to municipalities and districts
(Gheorghe 2005). Moreover, ‘the method, algorithm, and software are generic, and
are believed to accommodate a virtually unlimited variety of applications’
(Gheorghe and Vamanu 2004, p. 613). Adopting and adapting the QVA model for
the transportation system case came as a natural choice that serves our declared goal
of suggesting new approaches to tackle the emerging and yet not fully grasped issue
of vulnerability assessment in complex and interconnected systems.
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Keating, C. B., Katina, P. F., & Bradley, J. M. (2014). Complex system governance: Concept,
challenges, and emerging research. International Journal of System of Systems Engineering, 5(3),
263–288.
Risken, H. (1996). The Fokker-Planck equation: Methods of solution and applications. New York,
NY: Springer Science & Business Media.
Thom, R. (1975). Structural stability and morphogenesis. Reading, MA: Westview Press.
Ursu, I., Vamanu, D., Gheorghe, A., & Purica, I. I. (1985). Socioeconomic risk in development of
energy systems. Risk Analysis, 5(4), 315–326.
Vamanu, D. V., Gheorghe, A. V., & Vamanu, B. I. (2003). On a generic model in quantitative
vulnerability assessment. Romanian Journal of Physics: Supplement, 48, 229–237.
Chapter 8
An Illustrative Example—The Case
for Aarau-Zurich
Abstract This chapter provides a real-world case scenario in which a transportation system is selected and analyzed for hot spot using basic information.
8.1
Transportation Description
Name: Aara-Zurich
Number of TRIPS: 3
Total Length (km): 57.1
Number of RAIL TRIPS: 1
Total Length on RAIL (km): 43.9
Number of ROAD TRIPS: 2
Total Length on ROAD (km): 13.2
Figure 8.1 is a composite rendering of complementary distribution function
(CDF) for each of the TRIPS in the transportation system for Aarau-Zurich.
TRIP—color correspondence
TRIP: ‘S0 Aarau-Zurich 35 t’
TRIP: ‘S1 Zurich’
TRIP: ‘S2 Zurich 5 t’
8.1.1
Graph Coordinate Axis Limits
Probability Range (Y-axis): 10−11–10−4
Fatalities Range (X-axis): 100–105
The origin is in the LOWER-LEFT corner.
Probability:
min: 0.0000001
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6_8
163
164
8 An Illustrative Example—The Case for Aarau-Zurich
Fig. 8.1 Complementary
distribution function for three
trips: ‘S0 Aarau-Zurich 35 t’,
‘S1 Zurich’, ‘S2 Zurich 5 t’
max: 0.00001
Fatalities:
minGreen: 10
minRed: 10
med: 1000
max: 10,000
8.1.2
Transportation Statistics
• Highest Fatalities Expected: 4347 (persons) found in trip ‘S0 Aarau-Zurich 35 t’,
scenario ‘3D.SCO’, at Spot #7 located at CH-1903 coordinates (672,548.404,
251,157.088).
• Highest Affected Population: 71,262 (persons) found in trip ‘S0 Aarau-Zurich
35 t’, scenario ‘3E.SCO’, at Spot #8 located at CH-1903 coordinates
(680,750.874, 248,963.665).
• Highest Affected Area: 924.33 (ha) found in trip ‘S0 Aarau-Zurich 35 t’, scenario ‘3E.SCO’.
• Highest Probability of LOC: 0.000000084545447 found in trip ‘S2 Zurich 5 t’,
scenario ‘10.SCO’, at Spot #24 located at CH-1903 coordinates (685,743.189,
248,738.698).
• Lowest Fatalities Expected: 0 (persons) found in trip ‘S0 Aarau-Zurich 35 t’,
scenario ‘10.SCO’, at Spot #3 located at CH-1903 coordinates (648,875.958,
249,764.86).
• Lowest Affected Population: 0 (persons) found in trip ‘S0 Aarau-Zurich 35 t’,
scenario ‘10.SCO’, at Spot #6 located at CH-1903 coordinates (657,349.61,
249,907.447).
• Lowest Affected Area: 0.22 (ha) found in trip ‘S1 Zurich’, scenario ‘5F.SCO’.
8.1 Transportation Description
165
• Lowest Probability of LOC: 0.00000000287421 found in trip ‘S2 Zurich 5 t’,
scenario ‘10.SCO’, at Spot #5 located at CH-1903 coordinates (684,804.213,
246,112.307).
8.2
Representation Maps of the Transportation
8.2.1
‘Aarau-Zurich’ TRANSPORTATION Map
Representation
The overall map of the transportation system is presented in Fig. 8.2, first without
back maps and then with back maps.
8.2.1.1
TRIP ‘S0 Aarau-Zurich 35 t’
A detailed description of trip ‘S0 Aarau-Zurich 35 t’ is presented.
A. Trip Description
Type: RAIL
Route Name: teza 0.rte
Length: 43,925.8105825169 km
Number of Scenarios: 27
The following Spot Definition Summary was used in Statistics Evaluation:
Route Length of Relevance: 100
Route Objects: OR Station OR Signal OR Switch
Fig. 8.2 An overall ‘Aarau-Zurich’ transportation map with ‘no back maps’ and ‘with back
maps’. LEGEND RED line(s)—RAIL trip. BLACK line(s)—ROAD trip
166
8 An Illustrative Example—The Case for Aarau-Zurich
Fig. 8.3 A CDF for TRIP
‘S0 Aarau-Zurich 35 t’ for
every LIMITED RISK AREA
Infrastructure: OR Dwelling Areas OR Dwelling Developments OR Recreational
Areas OR Railway Areas/Facilities
Population in the Affected Area > 1000 persons
B. Trip CDF’s
Figure 8.3 is a CDF rendering computed for TRIP ‘S0 Aarau-Zurich 35 t.’
Graph Coordinate Axis Limits
Probability Range (Y-axis): 10−11–10−4
Fatalities Range (X-axis): 100–105
The origin is in the LOWER-LEFT corner.
Probability:
min: 0.0000001
max: 0.00001
Fatalities:
minGreen: 10
minRed: 10
med: 1000
max: 10,000
C. Trip ‘S0 Aarau-Zurich 35 t’ Map Representation
A overall map representing a trip ‘S0 Aarau-Zurich 35 t’ is provided in Fig. 8.4.
D. Trip ‘S0 Aarau-Zurich 35 t’ Scenarios
D.1 Scenario 10.SCO
Substance: GASOLINE
Mass: 3500
Area Affected: 18.1
Event Type: BLEVE
Release Category: small release
Number of Spots: 8
8.2 Representation Maps of the Transportation
167
Fig. 8.4 ‘S0 Aarau-Zurich 35 t’ trip map with ‘no back map’ and ‘with back maps’
D.2 Scenario 11A.SCO
Substance: GASOLINE
Mass: 3500
Area Affected: 30.49
Event Type: Explosion, Lung Impairment
Release Category: small release
Number of Spots: 8
….. interrupt…
D.27 Scenario 9G.SCO
Substance: GASOLINE
Mass: 3500
Area Affected: 27.63
Event Type: Pool Fire
Release Category: small release
Number of Spots: 8
E. Trip ‘S0 Aarau-Zurich 35 t’ Statistics
• Highest Fatalities Expected: 4347 (persons) found in scenario ‘3D.SCO’, at Spot
#7 located at CH-1903 coordinates (672,548.404, 251,157.088).
• Highest Population Affected: 71,262 (persons) found in scenario ‘3E.SCO’, at
Spot #8 located at CH-1903 coordinates (680,750.874, 248,963.665).
• Highest Area Affected: 924.33 (ha) found in scenario ‘3E.SCO’.
• Highest Probability of LOC: 0.000000084278018 found in scenario ‘10.SCO’,
at Spot #3 located at CH-1903 coordinates (648,875.958, 249,764.86).
• Lowest Fatalities Expected: 0 (persons) found in scenario ‘10.SCO’, at Spot #3
located at CH-1903 coordinates (648,875.958, 249,764.86).
• Lowest Population Affected: 0 (persons) found in scenario ‘10.SCO’, at Spot #6
located at CH-1903 coordinates (657,349.61, 249,907.447).
• Lowest Area Affected: 0.95 (ha) found in scenario ‘1F.SCO’.
168
8 An Illustrative Example—The Case for Aarau-Zurich
• Lowest Probability of LOC: 0.000000023921421 found in scenario ‘10.SCO’,
at Spot #4 located at CH-1903 coordinates (652,269.566, 250,583.355).
F. Trip ‘S0 Aarau-Zurich 35 t’ Map Representation
Four trip maps are rendered as follows:
Current trip highlighted (yellow) in the transportation map (no background map).
Current trip highlighted (yellow) in the transportation map (with background map).
Current trip (no background map).
Current trip (with background map).
Notice that
1. The number of trip map renderings depends on whether background map is set
(both for one of the transportation’s trips and the current trip).
2. Rendering the bounding box involves:
(a) Transportation bounding box for transportation-related maps.
(b) Trip route bounding box for trips with no background maps.
(c) Trip background map bounding box for trips with background maps.
3. Hot Spots are also rendered on maps following:
(a) BLUE spots: ALL the spots of the Highest Affected Area Scenario (see
Section E above). Notice how this is represented in Fig. 8.5.
(b) RED spot: the spot of the Highest Fatalities Expected (see Section E
above). Notice how this is represented in Fig. 8.6.
Fig. 8.5 Trip ‘S0 Aarau-Zurich 35 t’ (yellow) in TRANSPORTATION
8.2 Representation Maps of the Transportation
169
Fig. 8.6 Trip ‘S0 Aarau-Zurich 35 t’ alone
8.2.1.2
TRIP ‘S1 Zurich’
A detailed description of trip ‘S1 Zurich’ is presented.
A. Trip Description
Type: ROAD
Route Name: teza 1.rte
Length: 7932.75131372962 km
Number of Scenarios: 27
The following Spot Definition Summary was used in Statistics Evaluation:
Route Length of Relevance: 100.12453
Route Objects: OR Crossing
Infrastructure: OR Dwelling Areas OR Dwelling Developments OR Industrial
Enterprises OR Recreational Areas OR Street Areas OR Railway Areas/Facilities
Population in the Affected Area > 1500 persons
B. Trip CDF’s
Figure 8.7 is a CDF rendering computed for TRIP ‘S1 Zurich.’
Graph Coordinate Axis Limits
Probability Range (Y-axis): 10−11–10−4
Fatalities Range (X-axis): 100–105
The origin is in the LOWER-LEFT corner.
Probability:
min: 0.0000001
max: 0.00001
Fatalities:
minGreen: 10
minRed: 10
med: 1000
max: 10,000
170
8 An Illustrative Example—The Case for Aarau-Zurich
Fig. 8.7 A CDF for TRIP
‘S1 Zurich’ for a
LIMITED RISK AREA
Fig. 8.8 ‘S1 Zurich’ map
with ‘no back maps’
C. Trip ‘S1 Zurich’ Map Representation
A overall map representing a trip ‘S1 Aarau-Zurich’ is provided in Fig. 8.8.
D. Trip ‘S1 Zurich’ Scenarios
D.1 Scenario 10.SCO
Substance: GASOLINE
Mass: 2000
Area Affected: 11.2
Event Type: BLEVE
Release Category: small release
Number of Spots: 14
8.2 Representation Maps of the Transportation
171
D.2 Scenario 11A.SCO
Substance: GASOLINE
Mass: 2000
Area Affected: 20.62
Event Type: Explosion, Lung Impairment
Release Category: small release
Number of Spots: 14
… interrupt…
D.27 Scenario 9G.SCO
Substance: GASOLINE
Mass: 2000
Area Affected: 17.25
Event Type: Pool Fire
Release Category: small release
Number of Spots: 14
E. Trip ‘S1 Zurich’ Statistics
• Highest Fatalities Expected: 3825 (persons) found in scenario ‘3D.SCO’, at Spot
#14 located at CH-1903 coordinates (684,570.055, 245,601.757).
• Highest Population Affected: 50,586 (persons) found in scenario ‘3E.SCO’, at
Spot #1 located at CH-1903 coordinates (681,804.598, 249,401.413).
• Highest Area Affected: 635.64 (ha) found in scenario ‘3E.SCO’.
• Highest Probability of LOC: 0.00000006179435 found in scenario ‘10.SCO’, at
Spot #9 located at CH-1903 coordinates (684,414.449, 245,347.14).
• Lowest Fatalities Expected: 0 (persons) found in scenario ‘12.SCO’, at Spot #5
located at CH-1903 coordinates (683,312.115, 248,122.57).
• Lowest Population Affected: 0 (persons) found in scenario ‘1F.SCO’, at Spot #5
located at CH-1903 coordinates (683,312.115, 248,122.57).
• Lowest Area Affected: 0.22 (ha) found in scenario ‘5F.SCO’.
• Lowest Probability of LOC: 0.000000014818107 found in scenario ‘10.SCO’,
at Spot #6 located at CH-1903 coordinates (683,360.049, 248,122.57).
F. Trip ‘S1 Zurich’ Map Representation
Trip maps are rendered in a sequel as follows:
Current trip highlighted (yellow) in the transportation map (no background map).
Current trip (no background map).
Notice that
1. The number of trip map renderings depends on whether background map is set
(both for one of the transportation’s trips and the current trip).
172
8 An Illustrative Example—The Case for Aarau-Zurich
Fig. 8.9 Trip ‘S1 Zurich’
(yellow) in
TRANSPORTATION with
‘no back maps’
Fig. 8.10 Trip ‘S1 Zurich’
alone with ‘no back maps’
2. Rendering the bounding box is set as follows:
(a) Transportation bounding box for transportation-related maps.
(b) Trip route bounding box for trips with no background maps.
(c) Trip background map bounding box for trips with background maps.
3. Hot Spots are also rendered on maps, as follows:
(a) BLUE spots: ALL the spots of the Highest Affected Area Scenario (see
Section E above). Notice how this is represented in Fig. 8.9.
(b) The RED spot: the spot of the Highest Fatalities Expected (see Section E
above). Notice how this is represented in Fig. 8.10.
8.2 Representation Maps of the Transportation
173
Fig. 8.11 A CDF for TRIP
‘S2 Zurich 5 t’ for a
LIMITED RISK AREA
8.2.1.3
TRIP ‘S2 Zurich 5 t’
A overall map representing a trip ‘S2 Zurich 5 t’ is provided in Fig. 8.11.
A. Trip Description
Type: ROAD
Route Name: teza 2.rte
Length: 5260.29058973529 km
Number of Scenarios: 27
The following Spot Definition Summary was used in Statistics Evaluation:
Route Length of Relevance: 100.12453
Route Objects: OR Crossing
Infrastructure: OR Dwelling Areas OR Dwelling Developments OR Industrial
Enterprises OR Recreational Areas OR Street Areas OR Railway Areas/Facilities
Population in the Affected Area > 1500 persons
B. Trip CDF’s
The following is the rendering of the CDF computed for TRIP ‘S2 Zurich 5 t’ for
every RISK AREA LIMITS considered.
Graph Coordinate Axis Limits
Probability Range (Y-axis): 10−11–10−4
Fatalities Range (X-axis): 100–105
The origin is in the LOWER-LEFT corner.
Probability:
min: 0.0000001
max: 0.00001
Fatalities:
minGreen: 10
174
8 An Illustrative Example—The Case for Aarau-Zurich
Fig. 8.12 Trip ‘S2 Zurich 5 t’ map with ‘no back maps’ and ‘with back maps’
minRed: 10
med: 1000
max: 10,000
C. Trip ‘S2 Zurich 5 t’ Map Representation
An overall map representing a trip ‘S1 Zurich 5 t’ is provided in Fig. 8.12.
D. Trip ‘S2 Zurich 5 t’ Scenarios
D.1 Scenario 10.SCO
Substance: GASOLINE
Mass: 500
Area Affected: 4.03
Event Type: BLEVE
Release Category: small release
Number of Spots: 24
D.2 Scenario 11A.SCO
Substance: GASOLINE
Mass: 500
Area Affected: 8.29
Event Type: Explosion, Lung Impairment
Release Category: small release
Number of Spots: 24
… interrupt…
D.26 Scenario 9F.SCO
Substance: GASOLINE
Mass: 500
Area Affected: 0.22
Event Type: Flare Fire
Release Category: small release
Number of Spots: 24
8.2 Representation Maps of the Transportation
175
D.27 Scenario 9G.SCO
Substance: GASOLINE
Mass: 500
Area Affected: 6.27
Event Type: Pool Fire
Release Category: small release
Number of Spots: 24
E. Trip ‘S2 Zurich 5 t’ Statistics
• Highest Fatalities Expected: 1781 (persons) found in scenario ‘3D.SCO’, at Spot
#8 located at CH-1903 coordinates (684,954.938, 246,413.875).
• Highest Population Affected: 22,050 (persons) found in scenario ‘3E.SCO’, at
Spot #7 located at CH-1903 coordinates (684,756.655, 246,214.987).
• Highest Area Affected: 255.96 (ha) found in scenario ‘3E.SCO’.
• Highest Probability of LOC: 0.000000084545447 found in scenario ‘10.SCO’,
at Spot #24 located at CH-1903 coordinates (685,743.189, 248,738.698).
• Lowest Fatalities Expected: 0 (persons) found in scenario ‘10.SCO’, at Spot #21
located at CH-1903 coordinates (685,569.204, 248,447.66).
• Lowest Population Affected: 0 (persons) found in scenario ‘5F.SCO’, at Spot
#20 located at CH-1903 coordinates (685,521.269, 248,400.902).
• Lowest Area Affected: 0.22 (ha) found in scenario ‘5F.SCO’.
• Lowest Probability of LOC: 0.00000000287421 found in scenario ‘10.SCO’, at
Spot #5 located at CH-1903 coordinates (684,804.213, 246,112.307).
F. Trip ‘S2 Zurich 5 t’ Map Representation
Four trip maps are rendered in the sequel as follows:
Current trip highlighted (yellow) in the transportation map (no background map).
Current trip highlighted (yellow) in the transportation map (with background map).
Current trip (no background map).
Current trip (with background map).
Note that
1. The number of trip map renderings depends on whether background map is set
(both for one of the transportation’s trips and the current trip).
2. Rendering bounding box is set as follows:
(a) Transportation bounding box for transportation-related maps
(b) Trip route bounding box for trips with no background maps
(c) Trip background map bounding box for trips with background maps.
176
8 An Illustrative Example—The Case for Aarau-Zurich
Fig. 8.13 Trip ‘S2 Zurich 5 t’ (yellow) with ‘no back maps’ and ‘with back maps’
Fig. 8.14 Trip ‘S2 Zurich 5 t’ map with ‘no back maps’ and ‘with back maps’
3. Hot Spots are also rendered on maps, as follows:
(a) BLUE spots: ALL spots of the Highest Affected Area Scenario (see
Section E above). Notice how this is represented in Fig. 8.13.
(b) The RED spot: the spot of the Highest Fatalities Expected (see Section E
before). Notice how this is represented in Fig. 8.14.
Appendix A
Tools and Techniques for PRA
and RAMs: A Primer
Master Logical Diagrams
Developed and intensively used in the area of nuclear power plants probabilistic
risk assessment (Atwood et al. 2003; Papazoglou and Aneziris 2003), master logical
diagrams (MLD) have gained wide range of applicability (Gheorghe et al. 2003,
2004).
The MLD technique is suitable for modeling relationship of different independent functional blocks of complex systems that contribute to the achieving of a final
goal (Gheorghe et al. 2000a). The use of an MLD heavily depends on analysis
performed either in failure or in success spaces (see Sect. 3.1). Building an MLD in
success space helps in depicting the way in which various functions and
sub-functions of the system interact to achieve an overall system objective.
Building an MLD in failure space helps in the logical representation of the causes
for failure and identification of the initial disruptive events could lead into failure
state. Consequently, an MLD is hierarchical, top-down (or left-to-right) rendering
of initiating events, showing one or more general types of undesired events at the
top (left), moving toward an increasingly detailed event description at lower tiers
and displaying initiating events at the bottom (right).
Event Tree Analysis
Event tree analysis (ETA) is an assessment procedure which starts with an initiating
event and depicts the possible sequence of events that can lead to an accident. ETA
has also been described as a tool to identify all consequences of a system that have a
probability of occurring after an initiating event. It has a wide range of applications
including nuclear power plants, spacecraft, and chemical plants (Hong et al. 2009).
Thus, ETA qualifies as an intuitive tool for developing a tractable model for
important paths leading from an initial event to the end states of a given system.
Similar to MLD technique, ETA has its origins in the US Nuclear Regulatory
Commission risk assessment for nuclear power plants (Rasmussen 1975). The
initial methodology underwent through several revisions that transformed into a
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6
177
178
Appendix A: Tools and Techniques for PRA and RAMs: A Primer
more rigorous, mature, and accepted risk assessment tool in a variety of fields—
public and private.
At the base of ETA is an event tree (ET). An event tree is an inductive analytical
diagram used for identifying various possible outcomes of a given event (i.e., initial
event). An ET provides a visual representation of all the events which can occur in a
system, with a precise mathematical representation associated with it. According to
Bedford and Cooke (2002), an event tree is a basic modeling technique which
provides an effective method of dissecting the operation of an arbitrary system or
process into critical events which can then be assigned probabilities of success or
failure.
A brief description of the generic ET terminology, adapted for Chap. 3, is
provided:
• Initiating event (i.e., triggering event): The initiating event is the ET’s first level
branch that precedes the rest of the events chain;
• Event: An event is a branch in the ET that links one state of the system to the
subsequent state. An event also encapsulates a variety of meanings. It may be an
‘actual’ event (e.g., overturning) or a system state (e.g., improperly loaded
lorry), or a circumstantial state (e.g., traffic complexity level), or a human action
(e.g., driver observing situation and acts accordingly), or a failure on demand;
• Chance node: a branching point at which a new event is introduced in an ET. It
represents a transition from one state to another.
• Terminal points: the last-level branches; an outcome of the initial event is
associated with each of the terminal points; thus, a terminal point corresponds to
either success (e.g., accident not happening) or failure (e.g., accident happens)
states of a given system.
• Branch (event) probability: a likelihood of occurrence of a given event, conditional on the occurrence of previous events.
• Pathway: a chain of events in an event tree beginning from an initiating event to
an event of interest. Pathway probability is the joint probability of occurrence of
an intersection of events belonging to the chain of events.
• Full pathway: a pathway from the initial event a terminal point.
• Critical pathway: a full pathway to a failure terminal point (i.e., the sequence of
events that drive the system into a failure state).
When a probability is computed based on an ET, one should correlate the ET
diagram with the correspondent equations set for getting a holistic understanding of
the computation assumptions and scheme. Figure A.1 provides a generic event tree.
The following can be noted about an event tree:
• An initial event is the most left on the box;
• The sequence of events (i.e., system or circumstantial states, human actions or
protective systems which, if occurring/fail would drive the system into a failure
state) are represented in the rest of the top boxes;
Appendix A: Tools and Techniques for PRA and RAMs: A Primer
179
Fig. A.1 A generic event tree
• The success and failure branches are represented by solid and dotted lines,
respectively, and are associated with each system state/protective/action;
• The success and failure terminal points are represented by gray verses black
indices.
To identify the critical pathways, and hence understanding the assumptions
behind the model, one should follow the solid line paths from the trigger event to
the end of the event tree (left-to-right). Following denomination in Chap. 3:
ki
pij
ð1 pij Þ
qk
the relative frequency of the initial event occurrence.
pij is the <success>/<yes> random variable value of the j chance node;
the i index relates to the associated event tree index.
the <failure>/<false> random variable value of the j chance node.
full pathway k probability.
The final probability P{} is computed as the sum of all the critical path probabilities qk as:
X
Pfg ¼
qk jcritical
k
In turn, each qk is a product between the pij ’s corresponding to the success/failure
sequence that put the system into a failure state. If one uses the event tree in Fig. A.1,
then one has two critical pathways—ending at 4 and 5. Consequently:
Pffailurejtrigger g ¼ q4 þ q5
with
q4 ¼ ki ð1 pi1 Þ ð1 pi2 Þ pi3 ð1 pi4 Þ
q5 ¼ ki ð1 pi1 Þ ð1 pi2 Þ ð1 pi3 Þ
180
Appendix A: Tools and Techniques for PRA and RAMs: A Primer
and
ki
the relative frequency of the trigger event.
To get the accident scenario logics, one should read the event tree with the
Boolean algebra in mind. Thus, all events along a pathway are ANDed and all of
possible outcomes are ORed. Considering Fig. A.1 and assuming that the failure
event is accident, one can develop scenario accident using everyday language:
‘accident occurs if Event#1 does NOT occur AND Event#2 does NOT occur
AND Event#3 occurs AND Event#4 does NOT occur; OR Event#1 does NOT
occur AND Event#2 does NOT occur AND Event#3 does NOT occur. Naturally,
all of these must be preceded by the initial event occurrence.
Using Boolean logic, the ET equation becomes:
P ¼ ki
_
qk
qðkjcriticalÞ
with
k 2 f4; 5g
and
q4 ¼ :pi1 ^ :pi2 ^ pi3 ^ :pi4
q5 ¼ :pi1 ^ :pi2 ^ :pi3
Notice that in order to get pij correspondent meaning, one has to refer to the
graphical representation of the event tree.
Life Data Analysis: Weibull Distribution
Weibull analyses are used for failure rate estimation of components with
non-constant failure rate. Weibull analysis, sometimes referred to as Life Data
Analysis, originates from Professor Weibull (1951) theoretical paper on statistical
distributions. The appreciation of this approach came later Pratt and Whitney
applied in the analysis of defect data (Swingler 2014). Since then, Weibull analysis
is one of the most used methodologies in reliability engineering and failure analysis.
But what makes this analysis so attractive?
First, and in a more ‘statistical’ jargon, one can make predictions about product
life within a population by fitting a statistical distribution (i.e., Weibull) to life data
from a representative population. This distribution can then be used to estimate
important life characteristics of the product such as reliability or probability of
failure at given time. Second, as Abernethy notes, one of the main advantages of
Appendix A: Tools and Techniques for PRA and RAMs: A Primer
181
Weibull analysis is the ability to provide reasonably accurate failure analysis and
failure forecasts with extremely small samples (Abernethy 2006).
It is beyond the scope of this book to get into detailed description of generic Life
Data Analysis process. However, there exists a plethora of literature (e.g., see,
Abernethy 2006; Stamatis 2015; Swingler 2014) as well as freely online information on this subject. However, several aspects related to Weibull analysis that are
relevant to failure of transportation infrastructure components are depicted.
The first step in a Weibull distribution is the gathering of failure data. Failure
data must be recorded as a function of time or as any other variable influencing the
wear and tear of the product.
The function for modeling reliability, depicted as function of time, in Weibull
analysis is:
t c b
RðtÞ ¼ exp a
ðA:1Þ
with c; a and b calibration parameters, defined as:
c
a
b
location parameter, used to translate the plot along horizontal axis;
the scale (characteristic life) parameter;
the shape parameter.
The value of b holds the information about the time evolution of the failure rate
of a system. Thus, for b\1; the failure rate decreases with time, whereas for b [ 1;
the failure rate increases with time (Finkelstein 2008). One may also notice that for
b ¼ 1; and c ¼ 0; Eq. (A.1) yields a normal distribution.
The function of failure rate given by the Weibull function is:
kð t Þ ¼
b t cb1
a
a
Dorner (1999) also provides an online practical step-by-step tutorial of Weibull
Analysis using Microsoft Excel®.
References
Abernethy, R. (2006). The new Weibull handbook: Reliability and statistical analysis for
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Appendix B
Design Guidelines for Hazmat
Transportation Decision Support Systems
Conceptual Landmarks
Fundamentally, decision making is a process that implies:
1. Tackling objectives from different standpoints, sometimes divergent, or even
antagonist;
2. Working with large and sometimes ambiguous and huge volumes of data,
information, and knowledge;
3. Involving complex computational processes; and
4. Communicating the results in a variety of forms to relevant stakeholders who
tent to come from a different perspective than that of analysis/academic.
An executive expression of these issues involves Decision Support Systems
(DSS). A DSS, at a basic level, addresses a specific issue and offers (1) instruments
for assessing the consequences of different actions and (2) ways and means for
‘seeing’ the results of the assessment in a relevant manner that helps in choosing the
best (optimal) solution to the decision maker.
DSS complements human decisional capabilities with the computational power
of machines. In fact, there should always be a cooperative relationship between the
human factor and the power of DSS. On the one hand, humans are characterized by
the unique capability of reasoning, while on the other, machines provide faster data
manipulation and computational processes. Hence, it has been suggested that
machine offers assistance to the human decision maker to create a system that
considers the best of both aspects situations (Emery 1987). Certainly, these ideas
are not new and can be found in many different fields including sociotechnical
principles (Cherns 1987; Clegg 2000; Pyne 1997).
It has been noted that there can be a relative confusion when it comes to the
definition of a DSS (Louw 2002). Most ambiguity originates from different names
of DSS that are provided by different scientific communities in relation to software
tools designed for decision making. It appears that terms such as Management
Information System; Strategic Information System; Expert System; Intelligent
Decision Support System; and Decision Support System are applied interchangeably
at methodological and application levels.
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6
183
Appendix B: Design Guidelines for Hazmat Transportation …
184
In this section, we attempt to provide clarification in reference to current
research. A generic characterization of a DSS involves (Keen 1980):
• It is a useful tool for manipulating large quantities of information and computational processes in order to provide relevant information in decision-making
processes. A DSS should be seen as a tool which, under total control of the
decision maker, carries out complex data processing and computational tasks,
thus allowing the decision maker to focus on the non-formalizable aspects of the
decision-making process.
• DSS is a dedicated tool for providing support in solving a specific problem. It is
designed to address a specific decision-making process. The functionality of a
DSS must be consistent with the environment in which the analysis takes place.
• The DSS will not solve the problem. The DSS should assist the decision maker by:
– facilitating the analysis of the consequences of all the alternatives; and
– facilitating in choosing the optimal solution.
• A DSS is not a ‘black box.’ The structure and functionality of a DSS should
allow the decision maker to understand phenomena being investigated as well as
the logic behind the assessment procedure. In a case of user interface, system
should be able to provide relevant information in every step of the assessment
process.
With respect to the implemented tasks, DSSs can be classified by the following
taxonomy (Power 2002):
•
•
•
•
•
Communication-driven DSS;
Data-driven DSS;
Document-driven DSS;
Knowledge-driven DSS;
Model-driven DSS.
Data-driven DSS (Data-oriented DSS) and model-driven DSS (Model-based
DSS) are relevant to decision making in hazmat transportation. These are described
in Table B.1.
Table B.1 Two types of DSS relevant for transportation of hazmat
DSS type
DSS description
Data-oriented
DSS
The purpose of such a system is to provide the ‘traditional’ data processing
capabilities (query-based) as well as new ways of information visualization
and analysis (data-mining). When combined with visual, interactive
interfaces, these systems are a powerful tool for getting insights into large
quantities of data. This type of DSS is mainly used in the visual analytics and
visual reasoning realm (Thomas and Cook 2005)
These systems are used for assessing consequences of various actions (choices
of decision maker) and/or events that are not a choice of the decision maker
(e.g., tsunami risk following an earthquake). Implementation of such systems
requires the development of a set of mathematical models for simulating the
behavior of the system or phenomenon under scrutiny (Makowski 1994)
Model-based
DSS
Appendix B: Design Guidelines for Hazmat Transportation …
185
Mathematical models are a constituent part of the DSS. The models are developed for the part of the decision-making process that can be formalized. Naturally, a
special attention is given to the validity of the model. One of the necessary conditions in having a proper model is gathering, processing, and verification of the
data specific to the assessed process/phenomenon.
In respect to their role, a model-based DSS may be classified into two classes:
descriptive (predictive) and prescriptive. A descriptive DSS is generally used for
the behavioral prediction of the system. The core of the descriptive systems is
simulation models. A simulation model takes input as an alternative (decision
variable) and provides as output as consequences of given alternatives. Hence, this
technique is suitable for comparative assessment of already-known alternatives.
Conversely, a prescriptive system has the role of providing the information
related to different choices that would drive the behavior of the system in a desired
direction. Prescriptive DSS is based on optimization techniques. The input in this
case is minimizing/maximizing the objective and the output is a set of alternatives
that would lead toward the proposed goal.
Therefore, one can conclude that a descriptive DSS provides a response to ‘…
what would happen if … while prescriptive DSS as providing the decision-maker ‘a
set of optimal actions in order to …’
DSS Architecture
There is no one generic recipe for the architecture of a decision support system.
However, there are several characteristics common to all architecture. From a
functional requirements perspective, a DSS must provide capabilities related to
control of the environment, control of phenomenology, control and management of
data, and control the assessment tools (Gheorghe 2005).
Control of the environment (i.e., theater of action) is acquired through the use
and implementation of geographical information system (GIS). The role of a GIS is
to provide spatial information relevant to the analysis process and to allow visual
and geographical representation of the analysis results.
The relationship between GIS and DSS has implications for the analysis. First,
one needs to keep in mind that GIS engine is responsible for visual rendering of
maps and performing spatial analysis tasks and second, in the importance of the
GIS datasets. Such datasets provide description in numerical format and offer
additional information characterizing the map features such as roads, land use that
are relevant in DSS.
Nowadays, there is a plethora of GIS solutions on the market, both open-source
and proprietary. The main issue when it comes to implementing such a system into a
DSS is the access to the geographical data which, in most of the cases, is restrictive.
Moreover, due to the inherent complexity of such spatial databases and the costs of
developing, processing and maintaining of the datasets, all geographical areas might
not be covered in one commercial dataset. Consequently, implementation of a
186
Appendix B: Design Guidelines for Hazmat Transportation …
versatile GIS, capable of consuming (i.e., use maps and perform statistics) from
virtually any source, is strongly recommended, especially when the DSS is oriented
toward real-time crisis management. This is also recommended for DSSs intended to
cope with scenarios located virtually ‘anywhere in the World’ – i.e. the theatre of
action is not spatially confined (as it is the case of a single city/area). Authors do not
suggest that the use of professional and comprehensive databases should be discouraged. On the contrary, what is suggested is to use any information sources
available and not be limited by specific datasets. However, one must note that
commercial datasets might not be available and, when available, they might not
cover the system/location of interest or the data provided (i.e. features) might not be
suitable/enough for the models employed.
Control of the phenomenology is acquired by a modular architecture of the DSS.
This enables the potential of enriching the assessment capabilities by plugging-in
new modules that serve different tasks. It is recommended to have a centralized
manager of system resources who can access to different modules. It is essential to
ensure that different modules of the DSS are able to interact, whenever necessary, to
ensure functionality of other modules.
Control and management of data assumes the existence of data libraries holding
information relevant to the assessment models. In designing a DSS, the implementation of the modules capable of managing these resources should also be considered.
In most cases, the higher the complexity of the implemented mode, the more
difficulties one will have in the subsequent assessment process. In this case, if there
is a need, use a user-friendly and intuitive interface. This is an issue that is handled
under controlling the assessment tools in which the design purposely considers
model complexity beforehand. It is also recommended provide the end user with all
necessary details regarding the assessment model and the results in different phases
of the assessment.
The four basic characteristics of a DSS architecture are presented in Fig. B.1.
Interestingly, the Model Base bares the main responsibility with respect to quality
Fig. B.1 Basic constituents
of a DSS
Appendix B: Design Guidelines for Hazmat Transportation …
187
of the assessment. However, notice that the results provided may be irrelevant and
even wrong if the input from the GIS engine and the Database is incorrect.
Moreover, both, at the input and the output of the Models Base, the geographical
and physical databases provide (1) data required for the assessment and (2) the
communication platform of the results.
GIS Relevance in Hazmat Transportation DSS
S. Panwhar states that a GIS is a computer-based tool for ‘mapping and analyzing
things that exist and events that happen on earth’ (Panwhar et al. 2000). GIS
technologies bring together database capabilities (i.e., queries and statistics) and the
benefit of mapping and spatial analysis provided by maps. These characteristics
make the difference between GIS and any other kind of information communication
system.
Certainly, GIS provides a set of tools that can be used in planning, decision
making, and operational management; also, GIS-based systems have a variety of
applications, targeting fields such as land-use management, global-warming impact,
regional and urban planning, environmental risk assessment, hazard management,
emergency preparedness and response, market studies, and agriculture (Goodchild
2010).
In the particular field of transportation planning and optimal routing for hazmat
transportation, GIS-based approach is indispensable since it offers a variety of
information (e.g., geographic, political, environmental) pertinent to validity of the
assessment process.
A functional GIS integrates five key components: hardware, software, data,
population, and analysis methods (Panwhar et al. 2000). Notice that under this
approach, data and population are seen as distinctive entities. This reasoning suggests that one might conclude that GIS has only four key components since
information about population could be considered as data.
GIS technologies have been intensively used alongside DSS to support decision
making. As a direct consequence, the term Spatial Decision Support Systems has
been introduced to suggest GIS that also accommodates DSS characteristics
(Gheorghe 2005; Vamanu 2006).
GIS has the unique characteristic of providing not only mapping capabilities but
also powerful analysis tools which can support operations of complex operations in
a natural and intuitive manner (Rajamani 2002). Taking advantage of a GIS ensures
that the DSS becomes flexible and more powerful. The combination of GIS and
DSS also leads to an improved access and communication of information. Rather
than simply being selectors of predefined alternatives, a decision maker becomes an
active participant in the analysis process (Rajamani 2002).
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Appendix B: Design Guidelines for Hazmat Transportation …
There are several advantages for using software platforms for risk and vulnerability assessment. In the area on hazmat transportation, especially GIS–DSS
implementation, it can be said that:
(a) GIS can serve input data provider as well as a platform for results visualization
and communication
(b) functional and operational coupling of the spatial data and models with
computational modules
(c) Provides various analysis techniques oriented toward decision-making
processes.
In a GIS, spatial information is kept in two formats: vector and raster. The
vector data are entities defined in an orthogonal x–y space or x–y–z for
three-dimensional systems. The raster data are saved in a cell matrix that forms a
grid. There are advantages and disadvantages associated with each format and
selecting is based on the type of information being carried and the application
consumes the information.
In a vector-based layer, the geographic entities are given by points, lines, and
polygons, with or without holes. The location of an object is given by its x–
y coordinates while a line is defined by a sequence of points. A polygon is defined
as a closed sequence of points. Points, lines, or polygons that are contained in a
given map are known as features while a set of attributes, numerical or linguistic
data, corresponds to each feature.
A raster layer holds information in a cell matrix (rectangular grid). If the
information is in a form of an image, a cell is named a pixel. Grids are organized in
lines and columns. Each cell is associated with a set of attributes such as land use
and elevation. Satellites and aerial photographs represent examples of raster layers.
In recent times, there has been increased interest in developing transportation
management systems and as a result, developers of GIS-based systems have
introduced transportation risk-oriented capabilities into GIS platforms. Such products are collectively known as transportation GIS (Mainguenaud 2000).
Transportation GIS (GIS-T) provides the shortest path between source and destination by the optimization of a set of objectives (e.g., distance, exposed persons).
Another class of GIS-T has been developed to address scheduling problems. In this
case, optimization techniques are also used in assessment. In this case, a time
dimension is added in the optimization parameters. GIS-T systems are now widely
used and implemented in many commercial positioning systems such as GPS—
Global Positioning System.
Data Relevance in Hazmat Transportation DSS
Any item or chemical which, when being transported or moved, is a risk to public
safety or is an environmental hazard, and is regulated by one or more of the
following organizations (HMCRP 2011):
Appendix B: Design Guidelines for Hazmat Transportation …
•
•
•
•
•
189
US Department of Transportation; Hazardous Materials Regulations;
International Maritime Organization; International Maritime Dangerous Goods;
International Air Transport Association; Dangerous Goods Regulations;
International Civil Aviation Organization; Technical Instructions; and
US Air Force ‘INTERSERVICE’ Manual, Preparing Hazmat for Military Air
Shipment.
Hazmat also includes any item or chemical which is reportable or potentially
reportable or noticeable as inventory under the reporting requirements of the
Hazardous Chemical Reporting or as an environmental release under the reporting
requirements of the Toxic Chemical Release Reporting: Community Right To
Know.
Hazmat includes chemicals with special characteristics which suggest that they
can cause harm to people, plants, or animals when they are released through
spilling, leaking, pumping, pouring, emitting, emptying, discharging, injecting,
escaping, leaching, dumping, or disposing to environment. This includes abandoned, discarded barrels, and containers that might contain harmful chemicals.
In the USA, the Hazardous Materials Information Resource System (HMIRS) is
a Department of Defense to serve as a central repository for Material Safety Data
Sheets (MSDS) for the United States Government military services and civil
agencies. It also contains value-added information input by the service/agency focal
points (HMCRP 2011). The value-added data include HAZCOM warning labels
and transportation information. The system assists federal government personnel
who handle, store, transport, use, or dispose of hazardous materials. Given the
sensitive matter of transportation of such goods, access to such data is restricted.
Nevertheless, the availability of such data in DSS analysis is critically in the
validity of GIS-based approach. In fact, information regarding incident where a
release or a suspected release of a hazardous material has taken place in transportation is freely available online (see, e.g., PHMSA—Pipeline and Hazardous
Materials Safety Administration).
The Models
The models implemented in a DSS must reflect objectives and the assessment type
for which the application has been developed. In the particular case of hazardous
materials transportation, a descriptive DSS that would also follow the assessment
methodology in the previous chapters should contain a set of models that mainly
target:
190
Appendix B: Design Guidelines for Hazmat Transportation …
• Probability assessment for loss of containment accident;
• Consequence assessment of such an accident (i.e., environmental, economic,
and health) impact of hazardous material release;
• Risk assessment by combining the results probability and consequence.
It is important to note that a simple collection of valid models that describe the
effects of loss of containment (fire, explosion, and toxicity) is far from being
enough to constitute a DSS. A decision-support system is always an inseparable
blending of models and dedicated software. Moreover, the results do not offer the
final decision. A decision maker still has to make a choice based on the results of
the model.
References
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Clegg, C. W. (2000). Sociotechnical principles for system design. Applied Ergonomics, 31(5),
463–477.
Gheorghe, A. V. (2005). Integrated risk and vulnerability management assisted by decision
support systems: Relevance and impact on governance (Vol. 8). Dordrecht, The Netherlands:
Springer.
Goodchild, M. F. (2010). Twenty years of progress: GIScience in 2010. Journal of Spatial
Information Science, 2010(1), 3–20. http://doi.org/10.5311/JOSIS.2010.1.32
HMCRP. (2011). Guidebook for conducting local hazardous materials commodity flow studies.
Washington, DC: Transportation Research Board.
Keen, P. G. W. (1980). Decision support systems: A research perspective (Sloan WP No. 1117-80
No. CISR No. 54). Cambridge, MA: Massachusetts Institute of Technology. Retrieved from
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Louw, R. E. (2002). Information systems analysis 488: Decision support systems (No. 1074205).
St. Louis, MO: University of St. Louis. Retrieved from http://www.umsl.edu/*sauterv/
analysis/488_f02_papers/dss.html
Mainguenaud, M. (2000). Query models and languages for geographical information systems.
In R. Laurini (Ed.), Advances in visual information systems (pp. 511–520). Berlin: Springer.
Makowski, M. (1994). Design and implementation of model-based decision support systems
(No. WP-94-86) (p. 39). Laxenburg, Austria: International Institute for Applied Systems
Analysis. Retrieved from http://www.iiasa.ac.at/publication/more_WP-94-086.php
Panwhar, S. T., Pitt, R., & Anderson, M. D. (2000). Development of a GIS-based hazardous
materials transportation management system: A demonstration project (No. UTCA Report
99244) (p. 43). Tuscaloosa, AL: University Transportation Center for Alabama.
Power, D. J. (2002). Decision support systems: Concepts and resources for managers. Westport,
CT: Quorum Books.
Pyne, J. C. (1997). A sociotechnical systems analysis of the approval process for a complex public
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Rajamani, J. (2002). Siting obnoxious facilities using an integrated GIS-DSS (No. CE394K). West
Sussex, UK: Persona Associates. Retrieved from http://www.persona.uk.com/barnfield/
NBAF_documents/NBAF-2-4.pdf
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Vamanu, B. I. (2006). Managementul riscurilor privind transportul substanţelor periculoase:
aplicaţii ale sistemelor dinamice complexe (Dissertation). Universitatea Politehnica Bucureşti,
Facultatea de Chimie Aplicată şi Ştiinţa Materialelor, Catedra de Inginerie Economică,
Bucureşti.
Appendix C
Implementation Guideline for Hazmat
Transportation DSS
This appendix covers guidelines for developing an integrated software platform for
risk and vulnerability assessment in the transportation of hazardous materials. The
intent is to ensure support for developing real-world applications.
Appendix B discusses architecture addresses for implementation of a prescriptive DSS-T that would accommodate models for risk and vulnerability assessment
methods. In this appendix, focus is placed on functional characteristics of such an
application. Note that implementation solutions such as database engine, programming languages are not the subject of this appendix.
The role of the proposed DSS is in essence to address risk and vulnerability
assessment for hazmat transportation from the new approach in the quantitative risk
assessment (Gheorghe et al. 2000a) based on the societal risk computation by
taking into account loss of containment accident occurrence frequency, loss of
containment consequence assessment, as well as spatial (geographical) information
that characterizes a transportation segment.
Furthermore, the system would accommodate a novel vulnerability assessment
perspective and thus providing the capability of a more comprehensive characterization of the transportation system by introducing components that are typically
considered to be external to process under examination. In the software design
perspective, N-Layer architecture is proposed and thus being subject to
separation-of-concerns principle.
DSS-T: Architecture and Constituent Blocks
Functional requirements for the proposed DSS-T model follow the generic DSS
structure described in Sect. B.2 and the accompanying Fig. B.1 and supportive of
Vamanu (2006) research. A four-layer architecture is proposed, each with the
following constituents:
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6
193
194
Appendix C: Implementation Guideline for Hazmat Transportation DSS
The Data Layer
The data layer is located at the persistence storage part of the DSS. Usually, a
database server is implemented at this level. The purpose of the database server is to
hold various required model input data and to save the results of assessment
processes.
It is beyond the scope of the current book to recommend particular database
technology or even a database design. However, we suggest three of the most
popular relational database management systems (RDBM) available that could be
used for implementing DSS-T: MySQL, PostgreSQL, and Microsoft SQL Server.
Consistent with the statement that a DSS is as good as the level up to which it
serves its purpose, even a simple, text-file system-based approach might be suitable
for implementing. An RDBM for DSS-T database system should contain chemicals
and geographical (spatial information) databases. Figure C.1 shows a basic structure of the proposed model for DSS-T architecture.
Certainly, the chemicals database is an essential component of the DSS-T. The
data are indispensable to both developing the scenarios source term and performing
consequence assessment of a LOC accident. The information required during the
source terms definition is related to the possible outcomes of a LOC event involving
a specific chemical, which entails a relevant selection of the consequence assessment models. An LOC consequence assessment model should make an intensive
use of chemical physical characteristics (e.g., specific heat, combustion heat) in the
physical effects computational phase. Also, in order to perform health impact,
Fig. C.1 DSS-T architecture and the constituent blocks
Appendix C: Implementation Guideline for Hazmat Transportation DSS
195
Table C.1 A list of information required for a chemicals database
Physical characteristics
Molar mass
Boiling temperature
Latent heat vapors
Specific heat liquid
Combustion heat
Vapor pressure at 4 °C
IDLH
TLV
STEL
ERPG 1, 2, 3
Probit a, b, n
Unit
(kg/kmol)
(°C)
(kJ/kg)
(kJ/kg/K)
(kJ/kg)
(mm Hg)
(mg/m3)
(mg/m3)
(mg/m3)
(mg/m3)
Physical effect model
Fire
Pool Jet BLEVE
Explosion
Acute intoxication
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
which is quantified in lethality number, the models employed require the probit
coefficients such as described in Sect. 4.1.
The de minimis information, as represented by the x, that should be included in
the chemicals database is depicted in Table C.1. This table portrays relationship
between the different models in Chap. 4 and the chemical-specific characteristic.
Another required database is the spatial database. Similar to the chemicals
database, specifications regarding data format and selection of effective GIS
technologies are beyond the scope of the current discussion. However, several
remarks are made concerning spatial information required for implementing DSS-T
as well as recommendations about publicly available data sources.
Spatial information required for an operational implementation of the models in
the previous chapters is given in Table C.2. Name for each of the spatial data
sources in the format [identifier_sd] is provided for further reference.
Naturally, one should not consider that the given data source in Table C.2 will be
found in a single spatial dataset (e.g., one shapefile). Rather, and as in most cases in
real-case applications, these data will be a collection of datasets in different formats,
covering different spatial areas, with different scales. Consistent with the abstraction
level of introducing a GIS-T, names are just an indication about the role of the
information contained.
Spatial Data Resources
The following is a list of available online resources that may serve as primary
datasets for developing a GIS-T. Selection and use of these resources is optional.
However, the reminder of this appendix addresses the development of GIS-T based
on information available in one or more of these resources.
196
Appendix C: Implementation Guideline for Hazmat Transportation DSS
Table C.2 Spatial information required for a spatial database
Database elements
Features
Source format
Geographical
Elevations
Land-use
Hydrology (lakes, reservoirs, rivers, floodable areas)
[elv_sd]
[lu_sd]
[inw_sd]
[riv_sd]
[fa_sd]
[eq_sd]
[roadnet_sd]
[railnet_sd]
[sicroad_sd]
[sicrail_sd]
[hvnet_sd]
[admin_sd]
[popplaces_sd]
[popdens_sd]
Infrastructure
Administrative
Census
Seismic areas
Road network
Railroads network
Sensitive infrastructure components (road)
Sensitive infrastructure components (rail)
High-voltage network
Administrative boundaries (country, region, etc.)
Populated places
Population density
First, it is important to consider copyright terms, usage, and references when
developing the application. There are specific terms to each of the resources and
they are often available online.
Natural Earth
– Relevant Web site: http://www.naturalearthdata.com/
Natural Earth (NE) is one of the most comprehensive and freely available
spatial datasets to data. NE started in 2008 as a project and was built through a
collaboration of many volunteers with the support of NACIS—North American
Cartographic Information Society.
Natural Earth acts like a hub for a plethora of raster and vector data. The
datasets are provided at three scales: 1:10, 1:50, and 1:100 km.
There are several advantages associated with Natural Earth. However, one of
the most completing advantages is the handiness of immediate data usability. This
is given by both the data formats and geographic projection where:
– All vector data are in ESRI shapefile format;
– All raster data are in georeferenced TIFF format;
– All data use the latitude–longitude geographic coordinate system in WGS84
datum.
Other key features include the use of thematic themes which are grouped in three
classes: cultural, physical (vector), and raster. ‘Terms of use’ is another great
advantage of Natural Earth data. NE allows one to use the maps in any manner,
including modifying the content and design, electronic dissemination, and offset
Appendix C: Implementation Guideline for Hazmat Transportation DSS
197
Table C.3 Relevant features of natural earth pertinent to current research
Themes
Description
Cultural
Countries—holding political (country) border lines; available at 1:10, 1:50, and
1:110 scales
First-order admin—holding provinces, states, etc., depending on each National
administrative organization; available 1:10 and 1:50 scales
Populated places
Urban areas
Rivers and lakes centerlines—available at 1:10, 1:50 and 1:110 scales
Lakes
Physical
printing. Errors, if found in the data, can also be reported to NE. In the present
research, Natural Earth relevant themes are provided in Table C.3.
The Natural Earth Web site offers a more compressive listing of available data
and ‘Use of Terms.’
The Digital Chart of the World/Vector Map Level 0
Availability
There is no longer an official Digital Chart of the World download location.
However, Digital Chart of the World (DCW) used to be freely available for
download at ESRI and Penn State University—currently unavailable. However,
DCW dataset on compact disk (CD) format is available for purchase from various
online vendors such as www.geocomm.com.
Vector Map (VMAP) Level 0 datasets are available on NIMA ftp sites; a more
convenient way of downloading the data is through a third-party Web site (e.g.,
www.mapAbility.com). mapAbility also provides a valuable resource for VMap 0
datasets installation as well as several visualization software packages. The VMap
Level 0 original format is VPF. However, a more ‘ready-to-use’ ESRI shapefile
format may be found on GISLAB (http://imincik.github.io/gis-lab/).
Description
DCW is probably the most comprehensive GIS global database publicly available.
It was originally developed by ESRI for the United States Defense Mapping
Agency (DMA) using DMA’s Operational Navigation Chart (ONC) series that is a
primary source. The scale of the coverage is 1:1,000,000. The DCW utilizes the
Vector Product Format (VPF) georelational data model. Detailed information on
DCW specifications can be found in MIL-D-89009 (Defense Mapping Agency
1992).
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Appendix C: Implementation Guideline for Hazmat Transportation DSS
DCW was last updated in 1992. It has been followed by the improved versions
in 1997 (VMAP Level 0 and Level 1). In the ‘airfields’ metadata section of the
USGS Global GIS, it states that ‘… Vector Map (VMap) Level 0 database represents the third edition of the Digital Chart of the World. (…) VMap Level 0 is a
comprehensive 1:1,000,000 scale vector basemap of the world. It consists of cartographic, attribute, and textual data stored on compact disk read only memory
(CD-ROM)’ (http://webgis.wr.usgs.gov/globalgis/metadata_qr/metadata/airfields.
htm#t3). Both DCW and VMap use decimal degrees in geographic coordinates
as well as the WGS84 datum.
The thematic layers available in VMap are: Political/Oceans, Populated Places,
Railroads, Roads, Utilities, Drainage, Drainage-Supplemental, Hypsography,
Hypsography-Supplemental, Land Cover, Ocean features, Physiography,
Aeronautical, Cultural Landmarks, Transportation structure, Vegetation, and Data
Quality (Snyder 1987).
In current research, the VMap may be a source for: [lu_sd], [inw_sd], [riv_sd],
[fa_sd], [roadnet_sd], [railnet_sd], [hvnet_sd], [admin_sd], [popplaces_sd].
Global Earthquake Intensity Zones Map—Global Seismic
Information Network
– Relevant Web site: http://www.pdc.org/
Global Earthquake Intensity Zones (GEIZ) map is world coverage of earthquake
intensity zones. The map was produced by the United Nations Environmental
Program/Global Resource Information Database (UNEP/GRID) in 1994 on the
basis of the World Map of Natural Hazards, published by Munich Reinsurance
Company—Geoscience Research Group (Munich Re) in 1988. It is available
through the Global Seismic Information Network (GSIN) of the Pacific Disaster
Center. Relevant dataset is available at http://www.pdc.org/geodata/world/
earthquake_zones.zip and the dataset is in the ESRI shapefile format.
The map of GEIZ classifies earthquake risk into several classes based on the
Mercalli intensity scale. Mercalli intensity scale (MM) is a seismic scale used for
measuring the intensity of an earthquake. The Mercalli scale quantifies the effects of
an earthquake on the Earth's surface, humans, objects of nature, and man-made
structures on a scale from I (not felt) to XII (total destruction). Table C.4 provides
classification of GEIZ and the corresponding MM levels.
USGS Gtopo-30 and SRTM-30
GTOPO30 is a global digital elevation model (DEM) with a horizontal grid spacing
of 30 arcsec (approximately 1 km). GTOPO30 is a product of the US Geological
Survey (USGS).
Appendix C: Implementation Guideline for Hazmat Transportation DSS
199
Table C.4 GEIZ earthquake classification along with corresponding MM grades
GEIZ
class
Corresponding
MM grades
Zone 0
V (five) and
below
Zone 1
Zone 2
Zone 3
Zone 4
Zone 10
MM grade effects description
I. Not felt except by a very few under especially favorable
conditions
II. Felt only by a few persons at rest, especially on upper floors
of buildings
III. Felt quite noticeably by persons indoors, especially on upper
floors of buildings. Many people do not recognize it as an
earthquake. Standing motor cars may rock slightly. Vibrations
similar to the passing of a truck. Duration estimated
IV. Felt indoors by many, outdoors by few during the day. At
night, some awakened. Dishes, windows, doors disturbed; walls
make cracking sound. Sensation such as heavy truck striking
building. Standing motor cars rocked noticeably
V. Felt by nearly everyone; many awakened. Some dishes,
windows broken. Unstable objects overturned. Pendulum clocks
may stop
VI (six)
VI. Felt by all, many frightened. Some heavy furniture moved; a
few instances of fallen plaster. Damage slight
VII (seven)
VII. Damage negligible in buildings of good design and
construction; slight to moderate in well-built ordinary structures;
considerable damage in poorly built or badly designed
structures; some chimneys broken
VIII (eight)
VIII. Damage slight in specially designed structures;
considerable damage in ordinary substantial buildings with
partial collapse. Damage great in poorly built structures. Fall of
chimneys, factory stacks, columns, monuments, walls. Heavy
furniture overturned
IX (nine and
IX. Damage considerable in specially designed structures;
above)
well-designed frame structures thrown out of plumb. Damage
great in substantial buildings, with partial collapse. Buildings
shifted off foundations
X. Some well-built wooden structures destroyed; most masonry
and frame structures destroyed with foundations. Rails bent
XI. Few, if any (masonry) structures remain standing. Bridges
destroyed. Rails bent greatly
XII. Damage total. Lines of sight and level are distorted. Objects
thrown into the air
Additional zone indicating main waterbodies
The dataset was developed over a three-year time span and ended in 1996 and is
an international collaborative effort led by USGS’s Center for Earth Resources
Observation and Science (EROS) and involved the National Aeronautics and Space
Administration (NASA), the United Nations Environment Program/Global
Resource Information Database (UNEP/GRID), the US Agency for International
200
Appendix C: Implementation Guideline for Hazmat Transportation DSS
Development (USAID), the Instituto Nacional de Estadistica Geografica e
Informatica (INEGI) of Mexico, the Geographical Survey Institute (GSI) of Japan,
Manaaki Whenua Landcare Research of New Zealand, and the Scientific
Committee on Antarctic Research (SCAR). USGS datasets are available for
download by tiles at: http://eros.usgs.gov/#/Find_Data/Products_and_Data_
Available/gtopo30_info.
SRTM-30 is an improved version of GTOPO30. SRTM30 documentation
(ICESat 2015) notes that ‘SRTM30 is a near-global digital elevation model
(DEM) comprising a combination of data from the Shuttle Radar Topography
Mission, flown in February, 2000 and the U.S. Geological Survey’s GTOPO30 data
set.’ This dataset resulted from collaborative efforts of NASE, National
Geospatial-Intelligence Agency (NGA) and participation of the German and Italian
space agencies. The SRTM-30 dataset is available for download at: http://dds.cr.
usgs.gov/srtm/version2_1/SRTM30/. SRTM-3 dataset is available for download at:
http://dds.cr.usgs.gov/srtm/version2_1/SRTM3/. SRTM-3 is a higher resolution
version of SRTM-30. The coverage resolution is three arc-seconds.
Concluding this section is Table C.5 which highlights spatial information
required for building a GIS-T along with articulated data sources.
Thus far, the following remarks can be made: First, one should notice that all the
information required for assessment is not directly available in spatial databases.
This suggests that there is need to obtain data from different venues, applying
various analytical and/or geoprocessing models with some assumptions. For
example, there is no dataset for floodable areas. However, one could use a ‘naïve’
approach that utilized [fa_sd]. This naïve approach would include generating a new
polygon feature shapefile by buffering the line shapefile representing rivers with a
30-m threshold. Another approach would be a much more complex model that uses
ETOPO-3 dataset and ‘flood’ the neighboring zones of a river up to a given
flooding height, followed by taking the fingerprint of the flooded areas and creating
a raster dataset.
There is a need to address heterogeneous character of various spatial datasets.
This is reflected in both the spatial information (i.e., the different geographic projections, datum) and the features datasets (e.g., two data sources targeting populated
places may have the name of the cities in data fields [NAME] and [NAM]). This
information must be ‘brought to a common denominator’ in order to be properly
used in assessment models.
Finally, authors reiterate that building a (spatial) database required for a DSS in
general and DSS-T in particular is anything but simple. It involves acquiring
existing data, analyzing it to see its match to your model requirements,
modifying/create new datasets, and many other operations that take time, require
skills, and last but not least human and financial resources. Thus, it might be
necessary to invest a considerable amount of resources including financial,
acquiring professional datasets, and professional GIS technologies and GIS
professionals.
Appendix C: Implementation Guideline for Hazmat Transportation DSS
201
Table C.5 A comprehensive list of information required for GIS-T
Classification
Information
Reference ID
Possible sources
Geographical
Elevations
[elv_sd]
Land-use
[lu_sd]
Hydrology (lakes, reservoirs,
rivers, floodable areas)
[inw_sd]
[riv_sd]
Seismic areas
Road network
[fa_sd]
[eq_sd]
[roadnet_sd]
Railroads network
[railnet_sd]
Sensitive infrastructure
components (road)
Sensitive infrastructure
components (rail)
High-voltage network
[sicroad_sd]
USGS-30
GTOPO-30
GTOPO-3
DCW
VMap0
NE Lakes
NE Rivers and Lakes
Centerlines
*
GEIZ
DCW
VMap0
DCW
VMap0
–
[sicrail_sd]
–
[hvnet_sd]
DCW
VMap0
NA Countries
NA First-Order
Admin
NA Populated places
NA Urban areas
DCW
VMap 0
NA Populated
places*
Infrastructure
Administrative
Census
Administrative boundaries
(country, region, etc.)
[admin_sd]
Populated places (cities, towns)
[popplaces_sd]
Population density
[popdens_sd]
*Derived datasets
– No available online source identified. Should be generated ad-hoc
The Other datasets
As previously mentioned, the data layer also acts as the repository for the assessment results. But does one perform a comparative assessment? And how does one
make a decision when there is only access to single result? Consequently, there
must be a way to save work/analysis and making it available for future references in
a DSS-T design.
Additionally, assessment procedures can be time consuming, involving complex
tasks. This has an effect on the analysis as well as the analysts. The analyst may
need to make several assumptions (and decisions) during data processing. Hence,
the capability of reusing parts of the computational chain becomes critical and must
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Appendix C: Implementation Guideline for Hazmat Transportation DSS
be considered as a functional requirement when designing a DSS-T: There must be
a capability to save assessment at different stages in the computational chain. This
issue can best be described as follows: consider a situation in which an analyst has
already computed the risk for a given transportation segment—a process which
involved probability of LOC and consequence assessment. Assuming that this
process took five (5) hours, if the analyst now needs to consider another scenario
(e.g., probability of flat tire), then the analyst has to spend an additional 5 h.
However, it is best if the design is easily modifiable for unanticipated scenarios.
This might involve changing limited sections of the design such as performing LOC
probability assessment again and maintaining (i.e., reusing) the consequence
assessment part.
The aforementioned issues are expression of ‘modularity’ requirement and serve
as subsequent advantages for a DSS. However, the realization of such advantages
requires placing special attention to the design phase and use of holistic thinking.
Consequently, a deep understanding of the employed analytical models, computational modules, and of the assessment workflow is must in order to properly
identify the reusable (intermediate) results.
The Data Access Layer
Present authors recommend the development of a Data Access Layer (DAL) for
design and implementation. This recommendation is made on the basis of difficulties brought by the need to use heterogeneous datasets and technologies lead to
this approach as an interface between the actual datasets and the Business layer of
current application.
A DAL, as the layer of a program, provides simplified access to data stored in
persistent storage. And even though there is no unified description when referring to
DAL and software development (e.g., see, Java versus Microsoft realms), the following general patterns are required for present efforts:
– Abstraction of data must be made for application in models
– There must be a ‘Separation of Concerns’ which could be done using a table
with List—Array of records; Table row—Record; Row item—Record property
– There must be an accommodation for multiple sources of information. Sources
can be defined such as NA_roads, Transportation_segment, or another source of
spatial data. Obviously, in such a case, the interface must be able to distinguish
the differences especially during execution and implementation
– Everything in a DSS-T architecture following Data Access layer must use the
same type of information representation regardless of the source data. The
consideration of this issue is to ensure that necessary analysis can take place
even if data are collected from difference sources
– There must be a tight control of databases. The tight controls ensure, for
example, consistency in saving data
Appendix C: Implementation Guideline for Hazmat Transportation DSS
203
– There must be increased security. Security concerned is always necessary when
dealing with datasets involving hazmat
– Ensure that the system adheres to philosophy of ‘Separation of Concerns’
A very simple definition of DAL states provides a set of methods allowing for
unified access to data stores (i.e., obtaining data from a data store, updating its data
and schema) via object access layers. There are clear benefits to the DAL approach
especially from the perspective of architecture. This advantage can be seen from
Java’s Data Access Object (Java DAO) which is used in business applications. The
oldest and most mature technique is to use the Java Database Connectivity (JDBC)
API, which provides the capability to execute SQL queries against a database and
then fetch the results, one column at a time. Java 2 Enterprise Edition (J2EE) offers
a newer persistence framework in the form of Entity Beans, a subset of the
Enterprise JavaBean (EJB) framework.
Design Principles of the Data Access Layer
The objective of a DAL is to provide data to one’s business objects without using
database-specific code. One can accomplish through exposing a series of data
access methods from the DAL that operate on data in the data-tier using
database-specific code without exposing any database-specific method parameters,
or return types, to the business tier. In this case, any time a business object needs to
access the data-tier, one uses a method calls in the DAL instead of calling directly
down to the data-tier. This pushes database-specific code into the DAL and makes
your business object database independent (Armstrong 2006). Data access layer
contains a GIS engine that ensures data compatibility while ensuring data are
accessible. The application logic layer (business) houses a variety of models necessary for GIS-T as well as models necessary for risk and vulnerability assessment.
Finally, the assessment tools layer is an interface that the analyst uses for data
management, definition of scenarios, and analysis of the results.
As a recommendation, a fully fledged Create, Read, Update, Delete (CRUD)
capability should be provided to the DSS platform. The modules handling the
CRUD features of the DSS are placed at the Data Access layer.
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Appendix C: Implementation Guideline for Hazmat Transportation DSS
References
Armstrong, D. (2006). .NET application architecture: The data access layer. Simple Talk: A
Technical Journal and Community Hub from Redgate. Retrieved from https://www.simpletalk.com/dotnet/.net-framework/.net-application-architecture-the-data-access-layer/
Defense Mapping Agency. (1992). Military specification digital chart of the world (DCW)
(No. MIL-D-89009). Springfield, VA: U.S. Defense Mapping Agency.
Gheorghe, A. V., Grote, G., Kogelschatz, D., Fenner, K., Harder, A., Moresi, E., et al. (2000a).
Integrated risk assessment, transportation of dangerous goods: Case study. Zurich,
Switzerland: Target: Basel-Zurich/VCL. ETH KOVERS.
ICESat. (2015). SRTM30 documentation. Retrieved December 1, 2015, from http://icesat.gsfc.
nasa.gov/icesat/tools/SRTM30_Documentation.html
Snyder, J. P. (1987). Map projections: A working manual (USGS Numbered Series No. 1395).
Geological Survey (U.S.). Retrieved from http://pubs.er.usgs.gov/publication/pp1395
Vamanu, B. I. (2006). Managementul riscurilor privind transportul substanţelor periculoase:
aplicaţii ale sistemelor dinamice complexe (Dissertation). Universitatea Politehnica Bucureşti,
Facultatea de Chimie Aplicată şi Ştiinţa Materialelor, Catedra de Inginerie Economică,
Bucureşti.
Appendix D
Arriving at Equation for State of a System
with many Bi-stable Entities
An Expert-Oriented Tutorial1
Ever since the first introduction of the Quantitative Vulnerability Assessment
(QVA) model by Gheorghe and Vamanu (2004b), referenced at Sect. 7.1 of this
book, interested students as well as practitioners have, on several occasions,
expressed discomfort with trying to get to grips with the deductive
algebraic/calculus flow that takes them from one equation to other until eventually
arriving at the right, rather, compact analytic solution for the equation of state of
systems with multicomponent systems with bistable entities. Namely;
tanh
uf þ m
¼ 2f
H
ðD:1Þ
The tutorial that follows, although presumptuous about readers’ level of mathematical proficiency and inelegant by all academic standards, is the authors’ honest
attempt to meet such concerns. Readers satisfied with the explanatory discourse in
Sect. 7.1 may as well ignore this appendix.
1. Consider a dynamic system made of a large number, M, of bistable entities.
Assume that M1 entities are, at a given moment in time, in ‘State 1’—e.g., the
normal state or functional state; and that M2 entities are in ‘State 2’—e.g., the
abnormal state or dysfunctional state. This forms the basis for Eq. (D.2):
M ¼ M1 þ M2
ðD:2Þ
It comes natural to contend that the dynamics of the system consists, at the
elemental (or ‘atomic’) level, of an entity collapsing from State 1 into a State 2—
which takes the number M1 down to M1 1 and M2 to M2 þ 1; or conversely—
ascending from State 2 up into State 1—which takes M2 to M2 1 and M1 to
M1 þ 1: The fundamental lack of knowledge on when such an act takes place
1
Made available by the kind contribution of Dr. Dan V. Vamanu.
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6
205
206
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
induces the common recourse to probabilities: assume, therefore, that
w21 ðM1 ; M2 Þ is the probability of a State 1 to State 2 transition, whereas
w12 ðM1 ; M2 Þ is the probability of a State 2 to State 1 transition, where both
probabilities are some functions of M1 and M2 (see, the D.3 scheme).
ðD:3Þ
What the (D.3) scheme graphically depicts, a customary routine in Physics
translates into a ‘master equation’ for the distribution function, f ðM1 ; M2 ; tÞ; of
the probabilistic process described in (D.4)—a quantity that depends, as intuitively expected, on the current populations M1 and M2 ; while also varying with
the time, t.
@f ðM1 ; M2 ; tÞ
¼ w21 f ðM1 1; M2 þ 1Þ þ w12 f ðM1 þ 1; M2 1Þ
@t
ðw21 þ w12 Þf ðM1 ; M2 Þ
ðD:4Þ
In plain words, Eq. (D.4) tells us that the variation in time of the distribution
function—the left-hand side of the master equation—covers, in the integrative
manner provided by the concept,
(i) the acts of transitions from State 1 to State 2—the first term on right-hand
side of Eq. (D.4);
(ii) the acts of transitions from State 2 to State 1—the second term on
right-hand side of Eq. (D.4); and
(iii) would naturally depend also on the current state of the system, appropriately characterized by the ðM1 ; M2 Þ pair of numbers.
2. To make the master equation useful, one has to take it to a form amenable to an
algebraic handling. First, one operates a change of variables Eq. (D.5):
f¼
1 M1 M2 M1 M2
¼
2 M1 þ M2
2M
ðD:5Þ
To see the meaning in it, let us take the system to its limits: indeed, if one
assumes that all entities have somehow got into State 1 (‘functional’), therefore
making M1 ¼ M and, by way of consequence, making M2 ¼ 0 in Eq. (A.5), the
variable f takes the value 1/2. Conversely, if one assumes that all entities get in
State 2 (‘dysfunctional’), then, by making M2 ¼ M and, of course, M1 ¼ 0
variable f becomes −1/2 (scheme (A6)). In-between the extremes, variable f
would indeed work as a telling measure of system functionality, opposing the
functional population of entities, M1 to the dysfunctional population, M2 .
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
M1 ¼ M ! f ¼
1
2
1
M2 ¼ M ! f ¼ 2
207
ðD:6Þ
To take full advantage of the change of variable (D.5), the immediate obvious
consequences are worth noting:
M1 þ M2 ¼ M
M1 M2 ¼ 2Mf
M
1
þ Mf ¼ M
þf
2
2
M
1
M2 ¼ Mf ¼ M
f
2
2
ðD:7:1Þ
M1 ¼
1
1
1
þf 1 ¼ M
þf 2
2
M
1
1
1
f 1¼M
f
M2 1 ¼ M
2
2
M
ðD:7:2Þ
M1 1 ¼ M
ðD:7:3Þ
Upon these, one reaches the level of convenience that indeed justifies the change
of variable: all states of the system—the current, i.e., ðM1 ; M2 Þ; the functionally
depleted, i.e., ðM1 1; M2 þ 1Þ; and functionally enriched, i.e., ðM1 þ 1; M2 1Þ
can be algebraically represented by a single (as opposed to two) variable, f; along
with the constant M—the total population of entities in the system Eq. (D.8):
ðM1 ; M2 Þ
ðM1 1; M2 þ 1Þ
ðM1 þ 1; M2 1Þ
f
M2
2 þ 1Þ
f ¼ ðM1 1ÞðM
¼ M12M
M1 ¼ f M1
2M
ðM1 þ 1ÞðM2 1Þ
þ
M1 M2
f ¼
¼ 2M þ M1 ¼ f þ M1
2M
ðD:8Þ
On using the notation f; f and f þ ; the master equation can be rewritten as:
@f ðfÞ
¼ w21 ðf Þf ðf Þ þ w12 f þ f f þ ðw21 þ w12 Þf ðfÞ
@t
ðD:9Þ
Which, explicitly, reads:
@f ðfÞ
1
1
1
1
¼ w21 f f f
þ w12 f þ
f fþ
@t
M
M
M
M
ðw21 þ w12 Þf ðfÞ
ðD:10Þ
208
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
Featuring a single variable, f, Eq. (D.10) is now ready for more comprehensive
interpretations.
3. Of a first evidence is the fact that according to the original assumption that the
number M of system constituents is large, all functions involving its inverse,
1=M—a small quantity—in the right-hand side of Eq. (D.10) may be expressed
by standard, convergent series expansions than could safely be cut off at their
terms in the second order of 1=M :
@f ðfÞ
¼
@t
1 @w21
1 @ 2 w21
1 @f
1 @2f
f
w21 þ
þ
M @f
2M 2 @f2
M @f 2M 2 @f2
1 @w12
1 @ 2 w12
1 @f
1 @2f
þ
þ
f
þ
ðw21 þ w12 Þf
þ w12 þ
M @f
2M 2 @f2
M @f 2M 2 @f2
ðD:11Þ
Straightforward multiplications in the right-hand side of Eq. (D.11), followed by
ignoring all resulting terms of an order greater than 2 in 1=M (i.e., 1=M 3 or
1=M 4 ) and a regrouping of the resulting terms, will now make the contributions
to the time-partial-derivative of the distribution function f in the left-hand side be
arranged by their order in 1=M; as indicated in the chain of equalities
Eq. (D.12), next:
@f ðfÞ
1 @f
1 @2f
¼ ðw21 w12 Þ
þ ðw21 þ w12 Þ
@t
M @f
2M 2 @f2
2
1 @w21 @w12
1 @f @w21 @w12
1
@ w21 @ 2 w12
þ
f
þ
þ 2
þf
@f
@f
M @f
M @f @f
2M 2 @f2
@f2
1 @
1 @
1 @
½ðw21 w12 Þf þ f ðw21 w12 Þ f ðw21 w12 Þ
¼
M @f
M @f
M @f
1
@2f
@f @
@2
ðw21 þ w12 Þ 2 þ 2
ðw21 þ w12 Þ þ f 2 ðw21 þ w12 Þ
þ
2M 2
@f @f
@f
@f
2
1 @
1 @
¼
½ðw21 w12 Þf þ
½ðw21 þ w12 Þf M @f
2M 2 @f2
@ 1
1 @
@f
ðw21 w12 Þf ðw21 þ w12 Þ
¼
@f M
2M 2 @f
@f
ðD:12Þ
To make the long story short, Eq. (D.12) may now be written as:
@f
@J
þ
¼0
@t
@f
ðD:13Þ
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
209
which is a manner of evidencing a quantity, J, known in Physics as a ‘current’:
J¼
1
1 @
ðw21 w12 Þf ½ðw21 þ w12 Þf M
2M 2 @f
ðD:14Þ
In keeping with the same tongue/thinking, Eq. (D.13) indicates that the probability distribution function f is subject, in the inner dynamics of the system, to a
‘law of conservation.’
4. It is time now for assumptions that transcends the mere Algebra: The system is
assumed to find itself in a stationary state (i.e., a state in which the probability
distribution function, f, does not vary in time), which reads:
@f
¼0
@t
ðD:15:1Þ
By virtue of Eq. (D.13), the condition in Eq. (D.15.1) automatically entails that
the ‘current’ J does not vary with the ‘system operability fraction’—as we have
termed z, which in turn reads:
@J
¼0
@f
ðD:15:2Þ
Further on, the first derivative of the current J being nil entails that the ‘current’
J itself assumes a constant value, in the stationary state of the system:
J ¼ constant
ðD:15:3Þ
and, moreover, nothing would prevent us to take this arbitrary constant as being
zero.
So, let us have a recap of the last reasoning:
@f
@J
¼0!
¼ 0;
@t
@f
J ¼ constant;
constant ¼ 0
ðD:16Þ
5. We are now back to some algebra: given the expression in Eq. (D.14) of the
‘current’ J, the condition J ¼ 0 [see Eq. (D.16)] reads in fact:
ðw21 w12 Þf ¼
1 d
½ðw21 þ w12 Þf 2M df
ðD:17Þ
Note that the system’s stationary condition assumed allows us to replace partial
derivatives by straight derivatives.
210
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
Observe now that we can equally write Eq. (D.17) as:
w21 w12
1 d
ðw21 þ w12 Þf ¼
½ðw21 þ w12 Þf 2M df
w21 þ w12
ðD:17:1Þ
The petty trick of multiplying the left-hand side of Eq. (D.17) by
ðw21 þ w12 Þ=ðw21 þ w12 Þ—which actually means by 1—will prove more useful
than one may first realize: indeed, if we introduce now a new function, g,
relating to f as:
g ¼ ðw21 þ w12 Þf
ðD:17:2Þ
then we can easily rewrite Eq. (D.17.1) as:
w21 w12
dg
g¼
df
w21 þ w12
ðD:17:3Þ
dg
w21 w12
¼ 2M
g
df
w21 þ w12
ðD:18Þ
2M
or, which is the same thing, as:
And thus, we have ourselves an ordinary differential equation describing the
stationary state of the system.
We are now three steps away from integral solution of this equation. It goes like
this:
Step 1: change places of g and df in Eq. (D.18):
dg
w21 w12
¼ 2M
df
g
w21 þ w12
Step 2: integrate both members in the Step 1 results in Eq. (D.19); recall your
math:
– the primitive of 1=g is ln g;
– ln A ln B ¼ lnðA=BÞ;
– if ln g ¼ C
– then g ¼ eC
Note also that C is a constant that will remain inconsequential in the
further reasoning.
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
Zf
dg
¼ 2M
g
12
Zf
12
f
ln gðkÞ 1 ¼ 2M
2
1
ln gðfÞ ln g 2
Zf
12
Zf
¼ 2M
12
211
w21 ðkÞ w12 ðk Þ
dk
w21 ðkÞ þ w12 ðkÞ
w21 ðkÞ w12 ðk Þ
dk
w21 ðkÞ þ w12 ðkÞ
w21 ðkÞ w12 ðk Þ
dk
w21 ðkÞ þ w12 ðkÞ
1
ln g ¼ ln C
2
Zf
ln gðfÞ ln C ¼ 2M
12
gð f Þ
¼ 2M
ln
C
Zf
12
w21 ðk Þ w12 ðkÞ
dk
w21 ðk Þ þ w12 ðkÞ
w21 ðk Þ w12 ðkÞ
dk
w21 ðk Þ þ w12 ðkÞ
Step 3:
Z
2M
g ¼ Ce
w21 ðkÞ w12 ðkÞ
dk
12 w21 ðk Þ þ w12 ðk Þ
f
At last, given the definition in Eq. (D.17.2) of function g, one obtains
the target-function f as:
Z
f
2M
f ðfÞ ¼ C e
12
w21 ðk Þ w12 ðkÞ
dk
w21 ðkÞ þ w12 ðkÞ
ðw21 ðfÞ þ w12 ðfÞÞ
ðD:19Þ
6. To get further on, one has to employ some more Physics (alas!..). An additional,
yet intuitively natural assumption is that one has to look for the extremal surface
of the probability density of states f, which would allow one to detect the areas
of maximal probability of system's real behavior. In math language, looking for
extremes of a function is to force its first derivative with respect to the relevant
variable—in our case f—to zero:
212
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
df ðfÞ
¼0
df
ðD:20Þ
with f given by Eq. (D.19).
Performing the derivative of f ðfÞ given by Eq. (D.19) is textbook material.
A full account of the operation may look like this:
2
6 2M
df ðfÞ
d 6
e
¼0! 6
df
df 6
4
2
d6
6e
df 4
2M
Z
3
w21 ðkÞ w12 ðk Þ
dk 7
12 w21 ðk Þ þ w12 ðk Þ
7
7¼0
7
w21 ðfÞ þ w12 ðfÞ
5
f
Rf w21 ðkÞw12 ðkÞ 3
Rf w ðkÞw ðkÞ
dk
2M w 21ðkÞ þ w12 ðkÞdk
w21 ðk Þ þ w12 ðkÞ
21
12
7
1
1
1
7
2
2
þ
e
5 w21 ðfÞ þ w12 ðfÞ
d
1
df w21 ðfÞ þ w12 ðfÞ
¼0
2
d6
6e
df 4
2M
ðD:21Þ
ðD:21:1Þ
2
3
Rf w21 ðkÞw12 ðkÞ 3
Rf w ðkÞw ðkÞ
dk
2M w 21ðkÞ þ w12 ðkÞdk
Zf
w21 ðk Þ þ w12 ðkÞ
21
12
7
w21 ðk Þ w12 ðkÞ 7
1
1
7¼ d 6
2
dk5 e 2
5 df 42M
w21 ðk Þ þ w12 ðkÞ
2
¼
d6
42M
df
12
Zf
12
¼ 2M
3
w21 ðk Þ w12 ðkÞ 7
dk5
w21 ðk Þ þ w12 ðkÞ
w21 ðfÞ w12 ðfÞ
w21 ðfÞ þ w12 ðfÞ
ðD:21:1:1Þ
0
0
d
d
1
w21 ðfÞ þ w12 ðfÞ
df w21ðfÞ þ w12ðfÞ
¼
¼
df w21 ðfÞ þ w12 ðfÞ
½w21 ðfÞ þ w12 ðfÞ2
½w21 ðfÞ þ w12 ðfÞ2
ðD:21:1:2Þ
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
"
0
#
0
w21 ðfÞ w12 ðfÞ
1
w ðfÞ þ w12 ðfÞ
e
21
2M
w21 ðfÞ þ w12 ðfÞ w21 ðfÞ þ w12 ðfÞ ½w21 ðfÞ þ w12 ðfÞ2
2M
213
Rf w21 ðkÞw12 ðkÞ
1
2
w21 ðkÞ þ w12 ðkÞ
dk
¼0
ðD:21:2Þ
2M
w21 ðfÞ w12 ðfÞ
½w21 ðfÞ þ w12 ðfÞ
0
2
0
w21 ðfÞ þ w12 ðfÞ
½w21 ðfÞ þ w12 ðfÞ2
0
¼0
ðD:21:3Þ
0
w21 ðfÞ þ w12 ðfÞ
¼ 2M
w21 ðfÞ w12 ðfÞ
ðD:21:4Þ
In the equations above, apostrophes (') indicate first derivatives of the functions
w12 ðfÞ and w21 ðfÞ with respect to f:
7. At this stage, an analytic look into how the transition probability functions
w12 ðfÞ and w21 ðfÞ may look like can no longer be avoided. The solution is again
inspired by standard Statistical Physics: in physical systems of binary state
entities such as Ising, or Heisenberg magnets, where magnetic moments are
carried by ½ ‘spins,’ holding either ½ or −½ values, the transition probabilities
are assumed to depend on system’s state variable f as follows:
(
uf þ v
w12 ¼ wM1 e h ¼ wM
uf þ v
w21 ¼ wM2 e h ¼ wM
1
2
1
2
uf þ v
þ f e h
uf þ v
f e h
ðD:22Þ
with already-known notations, there are notable exceptions involving parameters u, v, and h in the exponentials.
To avoid becoming completely parochial, let us confine ourselves to loosely
saying that u, that multiplies the ‘system functionality variable’ f; is a measure
of the intensity of interaction between any two, closest-neighboring entities in
the system, whereas v is a measure of the interaction of entities with influences
outside the system, known as ‘fields.’ For more on these, we redirect the reader
to the main text in Sect. 7.1 and the accompanying references. On the other
hand, h is some measure of system’s ‘temperature’—that again should be
understood in the context as expanded upon in Sect. 7.1.
And now, back to elementary calculus: taking the first derivative of w12 ðfÞ and
w21 ðfÞ yields:
(
w012 ¼ wM 1 uh
w021 ¼ wM 1 þ
1
2 þf
u 1
h 2
uf þ v
e h
uf þ v
f e h
ðD:22:1Þ
214
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
Taking the expressions of w012 ; w021 from Eq. (D.22.1) and the expressions of w21
and w12 from Eq. (D.22) into the Eq. (D.21.4) of system’s surface of extremal
probability, one has:
wM 1 þ
u 1
h 2f
wM 12 f
e
e
uf þ v
h
uf þ v
h
þ wM 1 uh
wM
þf
1
2
e
1
2 þf
uf þ v
e h
uf þ v
h
¼ 2M
ðD:22:2Þ
Processing the fraction in (D.22.2) by simplifications and terms regrouping is,
again, textbook stuff. Here it is:
1 þ
u
h
h
1
2
u 1
h 2f
1
2f
f e
uf þ v
h
e
e
uf þ v
h
þ 1 uh
1
2
þ f e
1
2
f e
1
2
uf þ v
h
uf þ v
h
u
h
h
1
2
1
2
f e
i
e
uf þ v
h
¼ 2M
h uf þ v
i
uf þ v
e h e h
þ f e
uf þ v
h
e
uf þ v
h
uf þ v
h
þ f e
uf þ v
1
2
f e h 12 þ f e
h uf þ v
i
uf þ v
e h e h
¼ 2M
uf þ v
h
uf þ v
h
ðD:22:4Þ
¼ 2M
ðD:22:5Þ
1
2M
h
ðD:22:6Þ
i
¼u
h uf þ v
i
h uf þ v
i
uf þ v
uf þ v
e h e h f e h þ e h
1
h uf þ v
i
¼u
uf þ v
h 2M
e h e h
uf þ v
ðD:22:3Þ
i
uf þ v
h
e
1
2
uf þ v
h
1
2
h
þf
1
2 þf
uf þ v
e h
ðD:22:7Þ
uf þ v
1
e h þ e h
1
f uf þ v
uf þ v ¼ u
2
2M
h
h
e
e
h
1
uf þ v
1
f coth
¼u
2
h
2M
h
uf þ v
1
1
1
coth
¼
h
2 uh 2M f
ðD:22:8Þ
Appendix D: Arriving at Equation for State of a System with many Bi-stable Entities
215
8. The last step into the chores requires substantive observation that, in the
right-hand side of Eq. (D.22.8), the second fraction in parenthesis has the large
number M as its denominator, overwhelming—at nonzero ‘temperatures’ h; a
zero-temperature being inconceivable anyway, the u=h term, which makes the
respective fraction negligible when compared to ½—the first in the same
parenthesis. If we ignore the said small fraction, this leaves us with:
coth
uf þ v
1
h
2f
ðD:22:9Þ
A simple inversion of the quantities in Eq. (D.22.9) now gives:
tanh
uf þ v
¼ 2f
h
ðD:23Þ
where we take the liberty of making the equality categorical, which, in light of
the arguments displayed in this Appendix, is believed to be defendable.
The readers may wish to recognize the result, (D.23), as the equation of state of
the system of binary state entities discussed in Sect. 7.1 of this book.
A final remark: neither the book authors, nor their associates quoted in relation
to the subject of this Appendix, are claiming or have ever claimed to originate
the way of thinking and methodological clues regarding how one arrives at the
equation for system state with many bistable entities. Those assets belong to
such highly noted (and duly quoted) predecessors such as Haken and Weidlich
in Synergetics, Thom in the Theory of Catastrophies; Bragg, Williams, Ising,
and Heisenberg in Physics; and many others as noted in the References. Our
only feat was to make the solutions work for our purposes.
Reference
Gheorghe, A. V., & Vamanu, D. V. (2004b). Towards QVA—quantitative vulnerability
assessment: A generic practical model. Journal of Risk Research, 7(6), 613–628. http://doi.
org/10.1080/1366987042000192219
Index
A
Aarau-Zurich, 163, 165, 167, 168
Academic, 2, 93, 183, 205
Accident, 12, 23, 27, 41
Acute intoxication, 80, 84, 86
Ambiguity, vii, 183
Architecture, 185, 186, 193
As Resilient As Society Permits (ARASP),
101, 120
B
Boiling Liquid Expansion, Vapors Explosion
(BLEVE), 61, 69, 166
Bragg–Williams approximation, 149
Business, 2, 113, 203
C
Chemicals, 1, 6, 58, 80, 82, 189, 194
Collision, 27–30, 42, 44, 91
Complementary Cumulative Frequency of
Fatalities (CCFF), 15
Complexity, 1, 99
Consequence, 11, 12, 59, 61, 66, 69, 72, 80,
121
Critical infrastructures, 1, 4, 92
Cumulative Frequency of Fatalities (CFF), 15,
19
D
Database, 12, 15
Decision support systems (DSS), 57
Deductive, 24, 41
Democratic principles, 93
Dependency, vii, 3, 4, 60, 92, 100
Derailment, 6, 27, 28, 32, 37
E
Emergency, vii, 81, 100, 113, 135
Environment, 12, 15, 35, 50, 58, 80, 81, 100,
137
Event Tree Analysis (ETA), 25
Explosion, 17, 72, 76
Exposure, 4, 61, 80, 84, 85, 93, 98
F
Fatalities, 15, 17, 57, 124, 164
Fire consequence, 59, 61, 65
Flare fire, 65, 174
Fragility, 4
G
Geographical information systems (GIS), 57
Governmental, 2
Great Tohoku Earthquake, 92
H
Hazardous material, 7, 11, 61, 69, 83
Hazardous Materials Transportation Act
(HMTA), 6
Hot spot, viii, 12, 13, 39
I
Index method, ix, 107, 112, 120
Inductive, 24
Instability region, 154
Interdependency, vii, 3, 149
L
Lac-Mégantic, 6
Lethality percentage, 15, 17, 19, 58, 60, 61, 64,
77, 78, 84, 85, 89
Loss of containment (LOC), 12, 14, 15, 17, 23,
43, 57, 128
Loss of containment probability, 15, 17
Low probability, high consequence, 12
© Springer International Publishing Switzerland 2016
B.I. Vamanu et al., Critical Infrastructures: Risk and Vulnerability Assessment
in Transportation of Dangerous Goods, Topics in Safety, Risk,
Reliability and Quality 31, DOI 10.1007/978-3-319-30931-6
217
218
M
Master Logical Diagrams (MLD), 177
Matrix method, 120, 121, 123
Measure of system functionality, 206
Mitigation factors, 17
P
Physical effects, 15, 58, 129, 130
Pool fire, 15, 61–64
Population density, 13, 124
Potential loss types, 126
Probability, 12, 23, 28, 29, 31–34
Protective systems state, 36, 51
Q
Quantitative Vulnerability Analysis (QVA),
103, 142, 145–147, 156
R
Reliability, 4
Resiliency, 4, 91, 92, 120
Risk, VII, 4, 11, 12, 14
Risk assessment, 11, 18, 91
Risk classification, 11, 126
S
Sensitive, 12, 118, 131
Simulation, 185
Sociotechnical, 183
Index
Spatial data, 12
Success/failure space, 24, 25
System state space, 146, 148, 154
Systems theoretic principle, 115
T
Threat, 91, 93–95, 97, 98
Toxicity, 4, 15, 82
Transportation, 6
rail, 27
road, 41, 42
Transportation corridor, 18, 97, 107, 112, 123,
145
Transportation system, 6, 57, 98, 112, 124, 156
indicators, 156
V
Vicinity type, 36, 37, 51
Vulnerability, 4, 93–95, 97–100, 107, 115, 121
Cybernetic model, 93–97
Physiologic model, 95, 116
Semantic model, 93
Sociologic model, 93
Vulnerability assessment, 97, 100, 103, 123,
155
Vulnerability propositions, 96
W
Weibull distribution, 180