Copyright by Azadeh Mostofi 2018 The Dissertation Committee for Azadeh Mostofi Certifies that this is the approved version of the following dissertation: Development of a New Decision-Based Framework for Risk Assessment and Management of Landslides Committee: Robert B. Gilbert, Supervisor Kenneth H. Stokoe II Ellen M. Rathje Larry W. Lake Charles M. Woodruff, Jr. Development of a New Decision-Based Framework for Risk Assessment and Management of Landslides by Azadeh Mostofi Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin December 2018 Dedication I would like to dedicate this work to my parents, who always supported me from their heart, through all levels of my education and life, even while they were 12,000 km away from me. I would like to appreciate them for teaching me perseverance, value of knowledge and education, and having a positive contribution in the world. Acknowledgements I would like to acknowledge Dr. Gilbert’s support, as my PhD supervisor, through these years of my PhD education. I appreciate his patience, encouragement and his valuable feedbacks on my work. I would like to appreciate my supervisor and the members of my dissertation committee (Dr. Stokoe, Dr. Rathje, Dr. Woodruff, and Dr. Lake) for their time to review my work and their valuable comments. I would like to thank the professors who I had the chance to take their classes and learn valuable lessons. I would like to thank Dr. Eidsvig (NGI), Dr. Harbitz (NGI), and Dr. Hermanns (NGU) for providing me with more references on Norway case study. I would like to appreciate the professors at LARAM-2017 summer school (Salerno, Italy), for their valuable lectures on the landslide risk assessment and management subject. I would like to appreciate my family for their support through my life. Also, I would like to thank my best friends, Mahdi, Hossein, and Cary, for their support and encouragements through my life in Austin. v Development of a New Decision-Based Framework for Risk Assessment and Management of Landslides Azadeh Mostofi, PhD The University of Texas at Austin, 2018 Supervisor: Robert B. Gilbert Landslide is a complicated multi-hazard event that can turn into a great disaster. Landslide risk assessment and management process involves decision making to find an optimal loss-mitigation approach. A good, representative decision analysis process relies on reasonably capturing all possible scenarios that would happen in a landslide event and assessing the probabilities. The nature of a wide range engineering problems, including landslide risk assessment and management, requires that decisions to be made based on limited information and in the face of extreme uncertainty. Bayesian updating method is a more rational approach to account for extreme events and data irrelevancy. In Bayesian, a prior sample space is assumed, the probabilities are then updated by the likelihood function based on historical data. This procedure makes the Bayesian approach capable of accounting for extreme events and data irrelevancy. The prior sample space has a significant effect on updated probability distribution, especially in the case of rare or limited data. The main motivation of this research is to defensibly account for the uncertain in extreme events without unrealistic and unnecessary assumptions. Therefore, in this research, new decision-based framework is introduced for establishing non-informative prior sample space as a starting point in assessing the probabilities. In addition, this vi research introduces and applies new methods in the formulation of likelihood function in order to minimize the amount of unnecessary prescribed assumptions in the model. Two major risk management case studies are included in this dissertation: a rockslide in Western Norway, and the landslide in Oso, Washington. The objective of the case studies are to demonstrate the application of the new framework, introduced in this research to establish prior and formulate likelihood, in the real-world landslide risk assessment and management problems. These case studies showed that the framework suggested by this dissertation is a rational and defensible approach to account for the extreme uncertainties. The expected contribution of this research is in the field of risk assessment and management of landslides (or other natural hazards). The Decision Entropy is a theory underdevelopment toward becoming a rational method to establish non-informative prior sample space. The fact that the axioms of Decision Entropy Theory requires equally probable states for preference, degrees of preference, and information about preference of alternatives, makes this theory an impartial and objective approach to establish prior sample space in which no unnecessary assumption is included. Furthermore, axioms of this theory provide the tool to account for extreme events, unknown uncertainties, and irrelevancy of data in the risk analysis. However, the theory needs more development to make it easier to be used in the real-world risk assessment problem. Besides starting with a non-informative prior, the likelihood function should be formulated so that it does not include information more than what really is available. Using probability models that account for the renewal process of event, or accounts for the facts that events are non-stationary and correlated, has a greater advantage toward proper assessment of probabilities. Accounting for in-completeness and irrelevancy of data is also necessary to be considered in the formulation of likelihood function. vii Table of Contents List of Tables ........................................................................................................ xii List of Figures ...................................................................................................... xiv Chapter 1: Introduction ...........................................................................................1 Decision Analysis in the Face of Extreme Events ..........................................1 Motivation .......................................................................................................4 Objectives .......................................................................................................4 Methodology ...................................................................................................5 Expected Contributions ...................................................................................6 Organization of this Document .......................................................................6 Chapter 2: Background ...........................................................................................8 Introduction .....................................................................................................8 Landslide Risk ................................................................................................8 Landslide Risk Assessment and Management ................................................9 Methods of Probability Assessment..............................................................11 Classical (Frequentist) Statistical Method ....................................................12 Common Likelihood Functions ...........................................................12 Modeling Recurrence Time of Events ..........................................................15 Magnitude-Frequency Relationship .....................................................17 Bayesian Updating Method...........................................................................19 Bayesian Approach Compared to Frequentist Statistics ...............................20 Different Approaches to Establish Prior in Bayesian Analysis ....................22 Common Applications of Bayesian Approach in Landslide Problems ........24 Summary and Conclusion .............................................................................24 Chapter 3: Limitations of Existing Methods of Probability Assessment ..............26 Introduction ...................................................................................................26 Formulating Likelihood Function to Account for Correlation of Events .....29 Modeling Recurrence Time of Events ..........................................................30 Other Methods of Accounting for Nonstationary Events .............................31 viii Significance of Prior Probability Distribution in Bayesian Analysis ...........33 Example 1: Demonstration of the Significance of Prior Sample Space in Decision Analysis ................................................................................33 Summary and Conclusion .............................................................................37 Chapter 4: Methodology .......................................................................................38 Introduction ...................................................................................................38 Information Theory .......................................................................................38 Entropy in the Context of Information Theory .............................................40 Entropy of States ..................................................................................41 Entropy of Information ........................................................................43 Relative Entropy ..................................................................................44