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Risk and Safety in Civil Engineering Lecture Notes Prof. Dr. M. H. Faber 2007 Copyright © 2007 Michael H. Faber PREAMBLE Introduction The present script serves as study guidance for the students taking the course on Risk and Safety in Civil, Environmental and Geomatic Engineering. It provides information concerning the: (cid:2) Aim of the course. (cid:2) Structure and organisation of the course. (cid:2) Educational support material for the course. (cid:2) Mode of examination. (cid:2) Lecture notes for each of the 13 lectures with bibliography and index. Information about the contents of the course and the organization of the course is also available on http://www.ibk.ethz.ch/fa/education/ws_safety/ Aim of the course The aim of the present course is to provide to the students both the basic and more advanced skills and tools of risk and reliability in engineering. Emphasis is directed on the application and the reasoning behind the application of these skills and tools for the purpose of enhancing engineering decision making. It is expected that the students have prior knowledge on the subject of statistics and probability corresponding to the basic level of a bachelor of engineering. The purpose of the present course is thus to ensure that the students will acquire during the course the required theoretical basis and technical skills such as to feel comfortable with the theory, methods and application of risk and reliability analysis. Moreover, in the present course as opposed to many standard courses on the same subject, the perspective is to focus on the use of the theory for the purpose of engineering risk assessment and decision making. The course has been organized such that in the first five lectures the prerequisites for risk and reliability analysis are refreshed and the basics of risk assessment are given. In the following six lectures more advanced topics of reliability analysis and tools for reliability analysis are provided. Finally in the three last lectures applications are provided together with the topic of risk acceptance. i It is believed that students having completed the present course will be able to: (cid:2) Develop probabilistic engineering models for the purpose of risk assessment (cid:2) Formulate and perform decision analysis (cid:2) Structure and conduct risk assessments (cid:2) Perform reliability analysis for technical and structural components and systems (cid:2) Critically assess optimality and acceptability of decision alternatives Structure and organization of the course The course is conducted in the form of 13 weekly lectures. In addition to the lectures also exercises are available on http://www.ibk.ethz.ch/fa/education/ws_safety/ for the students to practice and apply their knowledge. It is assumed that the students will use approximately 90 minutes per week for self study per week. The student will have the possibility to seek assistance during weekly consultation hours which will be announced at the beginning of the course. Lectures: The lectures are targeted at providing the students with the most important aspects of the theoretical and methodical material which may also be found in the present lecture notes. However, the lectures will also focus on the philosophical background for the development and use of the theoretical background and are thus to be understood as partly complementary to the material of the lecture notes. It is assumed and strongly suggested that the students study and become familiar with the lecture notes. Educational support material for the course The course is supported by the present script which provides the theory being taught during the lectures. All material for the course will be made available partly prior to the start of the course and partly during the course on the home page http://www.ibk.ethz.ch/fa/education/ws_safety/ The course material contains besides the lecture notes also the Power Point presentations used for the lectures as well the solved exercises for each exercise tutorial. The lecture notes will be made available on the home page prior to the start of the course. The Power Point files of lectures will be uploaded on the course’s web page the latest one day before the respective lecture. ii The Power Point presentations are only meant as a support for the lectures and can be used only as a support for the learning and preparation before each lecture. It is expected that the students read all the material contained in the lecture notes from lecture to lecture. Reading the Power Point presentations is not a substitute for reading the lecture notes which in many cases provide more detailed information. Mode of Examination The present course is assessed through an oral examination. At the oral examination the main emphasis will be on the understanding of the topics in an engineering context. iii FOREWORD During the last decade there has been an increasing societal concern on sustainable developments focusing on the conservation of the environment, the welfare and safety of the individual and at the same time the optimal allocation of the available natural and economical resources of society. This problem complex may easily be realized to be a complex decision problem highly influenced by the possible consequences of our actions and the probabilities that these consequences will occur – the product of which is known as the risk. The continued development of society demands that we are able to manage the prevailing natural and manmade risks in a conscious, consistent and rational manner. According to fundamental principles of decision theory this is a prerequisite for the success of society. Managing risks is a matter of choice on how to allocate the available resources of society. A choice, which cannot be seen in isolation from the qualities on which we base society, e.g. the right to equal opportunities, education, welfare and safety. The question is and should always be – how can the resources of society best be allocated in accordance with these qualities. In this light risk management on behalf of society should be seen as a very serious matter and decision makers at all levels in society thus carry a tremendous responsibility. Risk management concerns the analysis, assessment and decision-making in regard to the risks involved in a given activity or associated with a given hazard. The risk management process includes the joint consideration of all uncertainties prevailing the problem and all possible consequences. Several important tasks are lying ahead, not least in the area of civil engineering. As always new civil engineering projects should be planned, designed and executed in a cost optimal manner taking into consideration the benefit of the projects as well as the possible adverse consequences such as loss of lives, damage to the environment and of course the direct costs. Future safeguarding, maintenance and decommissioning of the infrastructure of society will even more likely demand an intensified focus on risks. Not least in the view of the seemingly ongoing and expected climatic changes and the enormous efforts they may initiate to safeguard our existing infrastructure. The methods of risk and reliability analysis in civil engineering, mainly developed during the last three decades, are increasingly gaining importance as decision support tools in civil engineering applications. Their value in connection with the quantification and documentation of risks and the planning of risk reducing and mitigating measures is by now fully appreciated in the civil engineering profession. In the time to come the importance of risk and reliability methods will increase for the civil engineer – a fact reflected by the increasing normative and legislative requirements for the documentation of acceptable risks in the planning and execution of civil engineering activities. Risk and reliability analysis is in fact a multi-disciplinary engineering field requiring a solid foundation in one or several classical civil engineering disciplines in addition to a thorough understanding of probability, reliability analysis and decision analysis. iv The present book is meant to provide a basic understanding and insight to the issues of risk analysis in civil engineering and has been written on the basis of a set of my lecture notes for undergraduate students at the Swiss Federal Institute of Technology, ETH Zürich, having no or only little prior knowledge in the area. The material for the book has generally been collected from what I find the best parts of already existing literature, including textbook material, scientific publications and research reports. Based on my own experience from consulting engineering and participation in industry development and research projects I have attempted to present the material in a context and a form compatible with the “approach of the engineer”. Aiming at highlighting the decision problems and their possible solutions. The cost being that some mathematical precision is lost, the benefit – hopefully – being that the potential practical significance of the presented material is more obvious. It is important that the book is seen as an ongoing draft, evolving and hopefully improving from semester to semester. In pursuing this I gratefully acknowledge the help of my enthusiastic colleagues, Ph. D. students and assistants in my group. Zürich, September, 2007 Prof. Dr. Michael Havbro Faber v TABLE OF CONTENTS 1st Lecture – Engineering Decisions under Uncertainty 1.1 1.1 Introduction 1.2 Objective for Engineering Decision-Making 1.2 Societal Performance and Challenges 1.2 1.2 Introduction to Risk-Based Decision-Making 1.4 Example 1.1 – Feasibility of hydraulic power plant 1.4 1.3 Definition of Risk 1.7 1.4 The Risk-Based Decision Process 1.8 Define Context 1.8 Define System 1.10 Identify Hazard Scenario 1.10 Analysis of Consequences 1.10 Analysis of Probability 1.10 Identify Critical Risk Scenarios 1.11 Analysis of Sensitivities 1.11 Risk Assessment 1.11 Risk Treatment 1.11 Monitoring and Review 1.12 1.5 Detailing of Risk Analysis 1.12 1.6 Sources of Risk in Engineering 1.12 General Risks for Individuals 1.13 Risks Due to Natural Hazards 1.14 Risks Due to Malevolence 1.15 Risks Due to Structural Failures 1.16 The Role of Human Errors 1.17 Example 1.2 – Human error in bridge design 1.18 1.7 A Review of Reported Failures 1.19 Failures of Building and Bridge Structures 1.19 Failure of Dam Structures 1.24 Failures of Offshore Structures 1.25 Failures of Pipelines 1.27 Failures in Nuclear Power Plants 1.27 Failures of Chemical Facilities 1.28 2nd Lecture – Review of Basic Probability Theory and Statistics 2.1 2.1 Introduction 2.2 TOC-1 2.2 Definition of Probability 2.2 Frequentistic Definition 2.2 Classical Definition 2.3 Bayesian Definition 2.3 Practical Implications of the Different Interpretations of Probability 2.4 2.3 Conditional Probability and Bayes’ Rule 2.5 Example 2.1 – Using Bayes’ rule for concrete assessment 2.6 Example 2.2 – Using Bayes’ rule for bridge upgrading 2.7 2.4 Introduction to Descriptive Statistics 2.8 2.5 Numerical Summaries 2.9 Central Measures 2.9 Example 2.3 – Concrete compressive strength data 2.9 Dispersion Measures 2.10 Other Measures 2.11 Measures of Correlation 2.12 2.6 Graphical Representations 2.13 One-Dimensional Scatter Diagrams 2.13 Histograms 2.13 Quantile Plots 2.14 Tukey Box Plots 2.16 2.7 Introduction to Engineering Uncertainty Modelling 2.17 2.8 Uncertainties in Engineering Problems 2.18 2.9 Random Variables 2.20 Cumulative Distribution and Probability Density Functions 2.20 Moments of Random Variables and the Expectation Operator 2.22 Probability Density and Distribution Functions 2.22 The Normal Distribution 2.24 The Lognormal Distribution 2.25 Properties of the Expectation Operator 2.25 Random Vectors and Joint Moments 2.26 Conditional Distributions and Conditional Moments 2.27 2.10 Random Processes and Extremes 2.28 The Poisson Counting Process 2.28 Continuous Random Processes 2.30 Statistical Assessment of Extreme Values 2.31 Extreme Value Distributions 2.32 Type I Extreme Maximum Value Distribution – Gumbel max 2.33 Type I Extreme Minimum Value Distribution – Gumbel min 2.34 Type II Extreme Maximum Value Distribution – Frechet max 2.35 Type III Extreme Minimum Value Distribution – Weibull min 2.35 Return Period for Extreme Events 2.37 2.11 Introduction to Engineering Model Building 2.37 TOC-2 2.12 Selection of Probability Distributions 2.38 Model Selection by Use of Probability Paper 2.39 2.13 Estimation of Distribution Parameters 2.42 The Method of Moments 2.42 The Method of Maximum Likelihood 2.43 Example 2.4 – Parameter estimation 2.43 3rd Lecture – Bayesian Decision Analysis 3.1 3.1 Introduction 3.2 3.2 The Decision / Event Tree 3.2 3.3 Decisions Based on Expected Values 3.3 3.5 Decision Making Subject to Uncertainty 3.5 3.6 Decision Analysis with Given Information - Prior Analysis 3.5 3.7 Decision Analysis with Additional Information - Posterior Analysis 3.6 3.8 Decision Analysis with ‘Unknown’ Information - Pre-posterior Analysis 3.9 3.9 The Risk Treatment Decision Problem 3.10 4th Lecture – Risk Assessment in Civil Engineering 4.1 4.1 Introduction 4.2 4.2 The JCSS Framework for Risk Assessment in Engineering 4.2 Decisions and decision maker 4.3 Attributes of decision outcomes 4.5 Preferences among attributes - utility 4.5 Constraints on decision making 4.6 Feasibility and optimality 4.6 4.3 System Modelling 4.7 Knowledge and uncertainty 4.8 System representation 4.9 Exposure and hazards 4.11 Vulnerability 4.11 Robustness 4.11 4.4 Assessment of risk 4.12 Indicators of risk 4.13 Risk perception 4.14 Comparison of decision alternatives 4.15 Criteria for and acceptance of risk 4.16 Discounting and sustainability 4.16 TOC-3