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When planning flood protection, agencies are confronted with uncertainty in the design flood magnitude. In particular, the required capacity may increase in the future and render the protection insufficient. This problem can be adressed by applying a safety factor to the design capacity. We propose a Bayesian quantitative sequential decision model that identifies a cost-optimal safety factor in the face of uncertainty. It takes into account the flexibility of the protection system, that is, how costly it is to adjust. We focus on the description of the decision model and on the concept of flexibility, investigating only the effect of uncertainty from the historic flood record. Extension to other types of uncertainty is possible. The model is implemented for a catchment in Germany. Various degrees of uncertainty are investigated by using different lengths of historic records. The optimal safety factor decreases with decreasing uncertainty and with increasing system flexibility. K E Y W O R D SBayesian decision analysis, decision support under uncertainty, flexible protection strategies, flood protection, natural hazards, safety factor, uncertainty quantification

A probabilistic model for estimating tunnel excavation time is learnt with data from past tunnel projects. The model is based on the Dynamic Bayesian Network technique. The model inputs are determined through an analysis of data from three tunnels built by means of the conventional tunneling method. The data motivate the development of a novel probability distribution to describe the excavation performance. In addition, the probability of construction failure events and the delay caused by such failures are estimated using databases available in the literature. The model is applied to a case study, in which it is demonstrated how observations from the tunnel construction process can be included to continuously update the prediction of excavation time.

Cost-benefit analysis (CBA) is commonly applied as a tool for deciding on risk protection. With CBA, one can identify risk mitigation strategies that lead to an optimal tradeoff between the costs of the mitigation measures and the achieved risk reduction. In practical applications of CBA, the strategies are typically evaluated through efficiency indicators such as the benefit-cost ratio (BCR) and the marginal cost (MC) criterion. In many of these applications, the BCR is not consistently defined, which, as we demonstrate in this article, can lead to the identification of suboptimal solutions. This is of particular relevance when the overall budget for risk reduction measures is limited and an optimal allocation of resources among different subsystems is necessary. We show that this problem can be formulated as a hierarchical decision problem, where the general rules and decisions on the available budget are made at a central level (e.g., central government agency, top management), whereas the decisions on the specific measures are made at the subsystem level (e.g., local communities, company division). It is shown that the MC criterion provides optimal solutions in such hierarchical optimization. Since most practical applications only include a discrete set of possible risk protection measures, the MC criterion is extended to this situation. The findings are illustrated through a hypothetical numerical example. This study was prepared as part of our work on the optimal management of natural hazard risks, but its conclusions also apply to other fields of risk management.

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Abstract. Technical flood protection is a necessary part of integrated strategies to protect riverine settlements from extreme floods. Many technical flood protection measures, such as dikes and protection walls, are costly to adapt after their initial construction. This poses a challenge to decision makers as there is large uncertainty in how the required protection level will change during the measure lifetime, which is typically many decades long. Flood protection requirements should account for multiple future uncertain factors: socioeconomic, e.g., whether the population and with it the damage potential grows or falls; technological, e.g., possible advancements in flood protection; and climatic, e.g., whether extreme discharge will become more frequent or not. This paper focuses on climatic uncertainty. Specifically, we devise methodology to account for uncertainty associated with the use of discharge projections, ultimately leading to planning implications. For planning purposes, we categorize uncertainties as either “visible”, if they can be quantified from available catchment data, or “hidden”, if they cannot be quantified from catchment data and must be estimated, e.g., from the literature. It is vital to consider the “hidden uncertainty”, since in practical applications only a limited amount of information (e.g., a finite projection ensemble) is available. We use a Bayesian approach to quantify the “visible uncertainties” and combine them with an estimate of the hidden uncertainties to learn a joint probability distribution of the parameters of extreme discharge. The methodology is integrated into an optimization framework and applied to a pre-alpine case study to give a quantitative, cost-optimal recommendation on the required amount of flood protection. The results show that hidden uncertainty ought to be considered in planning, but the larger the uncertainty already present, the smaller the impact of adding more. The recommended planning is robust to moderate changes in uncertainty as well as in trend. In contrast, planning without consideration of bias and dependencies in and between uncertainty components leads to strongly suboptimal planning recommendations.

Long term decisions, such as the design of infrastructure systems and buildings or the planning of risk mitigation measures, should be made in consideration of the uncertain future. The initial design of a system determines its flexibility, i.e. its ability to cope with potential future changes. Increasing flexibility is generally considered to be a good approach to dealing with future uncertainty, such as climate change uncertainty, but its effects have not been systematically investigated. We propose the use of Markov Decision Processes combined with Influence Diagrams to solve adaptation planning problems. This framework can identify the optimal system type and capacity and determine the value of flexibility. It is here applied to two numerical examples: Planning of a waste water treatment plant under uncertainty in future population growth and planning of a flood protection system under uncertain climate change scenarios. Based on these idealized examples, it is shown that for flexible systems a lower initial capacity of the system is recommendable, while for inflexible systems a conservative design (with high safety factors) should be applied. The value of flexibility is shown to be high when significant learning is expected in the future, i.e. if information gathered in the future significantly reduces uncertainty.

Tunnel construction commonly causes deformations of the surrounding ground, which can endanger buildings and other structures located in the vicinity of the tunnel. The prediction of these deformations and damages to buildings is difficult, due to limited knowledge of geotechnical conditions and due to uncertainty in predicting the response of the structures to the settlements. This motivates the development of a probabilistic model for the prediction of tunneling-induced damage to buildings. We propose such a model, based on the classical Gaussian profiles for the approximation of the subsidence trough and the equivalent beam method for modeling the response of the building walls. In practice, settlements are commonly monitored through deformation measurements. To account for this, we present a Bayesian method for updating the predicted settlements when measurements are available. Finally, we show how maximum allowable settlements, which are used as threshold values for monitoring of the construction process, can be determined based on reliability-based criteria in combination with measurements. The proposed methodology is applied to a group of masonry buildings affected by the construction of the L9 metro line tunnel in Barcelona.