Internal erosion is a significant cause of failure in dams, levees and other hydraulic structures. This article studies the time-dependent reliability of such structures under Backward Erosion Piping (BEP), a form of internal erosion in the foundation. First, a physics-based time-dependent piping failure model is presented. Second, a time-variant reliability analysis method is presented which allows to quantify how the reliability evolves over the years due to cumulative pipe growth over multiple flood events. Finally, these models are used to study the importance of time-dependence for reliability estimates of flood defenses in The Netherlands. The findings show that, particularly in coastal areas, incorporating time-dependence significantly reduces the computed failure probability. Reductions vary widely, ranging from a factor of 5 to more than (Formula presented.) depending on flood duration and levee properties. Therefore, reliability estimates for levees can be improved by incorporating time-dependent pipe development in the BEP failure model, and thereby contribute to avoiding unnecessary reinforcements.

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Canal dikes in low-lying polders, as well as in other regions worldwide, are critical infrastructure for flood protection and water management. The subsurface water conditions can cause dike failures during excessive rainfall and prolonged periods of drought. There is a lack of multi-year monitoring of subsurface water conditions in canal dikes and an insufficient understanding of their geohydrological behavior. This study provides and analyses a novel multiyear data set of soil moisture and hydraulic heads (from February 2020 until March 2023) from a monitoring network covering various canal dikes with different characteristics in the western Netherlands. The data, including two extremely dry summers, highlight the impact of meteorological variations on the subsurface water conditions. Non-hydrostatic hydraulic head levels were observed during droughts that can be detrimental to dike stability and that are often not accounted for in safety assessments for drought situations. The effectiveness of various meteorological drought indicators applied to subsurface water conditions was evaluated: the precipitation deficit is the most reliable measure and outperforms the standardized drought indicators (SPEI and SPI). The drought recovery of dikes was analyzed to understand seasonal transitions and the sequence of different failure mechanisms, during dry and wet situations. This analysis also reveals differences between meteorological, soil moisture, and groundwater droughts, highlighting soil's storage capacity after drought and the limitations of meteorological drought indicators as proxies for soil moisture and groundwater. The insights from this study enhance assessments, inspection procedures and the identification of weak spots of dikes and other earthworks of infrastructure.@en

The management of water and flood risk levels in low-lying polder regions depends on the performance of canal dikes. Heavy rainfall can lead to peak hydraulic heads within the dikes affecting their stability, which can induce dike breaches. Variations in head responses and head statistics are both relevant for regional flood risk analysis of canal dike systems. This study examined the dynamics of peak heads in canal dikes on a national scale using time series models calibrated on observed heads. Various model structures are evaluated and a nonlinear model performed the best. These models were used to simulate long-term head time series. Subsequently, dike clusters were identified based on the coincidence of peak heads, allowing for the identification of dikes where peaks are caused by (dis)similar types of rainfall events. The differences and similarities in peak head response were related to physical dike characteristics. While no single significant relationship emerged, the soil type combined with the width of the dike appears to be important factors influencing the variation in head responses. However, the presence of the same soil type and dike widths in multiple clusters indicates that these characteristics do not yield a definitive outcome for the head response. Moreover, peak head statistics across various dikes were derived and indicated that extreme and yearly load conditions are relatively close to each other, with a median decimation height of only 15 centimeters. The head statistics are affected by climate change, characterized by increasing winter precipitation and summer evaporation. By 2100, extreme peak heads are expected to occur between 3 times less and 8 times more frequently, depending on the climate scenario and the type of canal dike.@en

Accurate estimation of extreme discharges in rivers, such as the Meuse, is crucial for effective flood risk assessment. However, hydrological models that estimate such discharges often lack transparency regarding the uncertainty in their predictions. This was evidenced by the devastating flood that occurred in July 2021, which was not captured by the existing model for estimating design discharges. This article proposes an approach to obtain uncertainty estimates for extremes with structured expert judgment using the classical model (CM). A simple statistical model was developed for the river basin, consisting of correlated generalized extreme value (GEV) distributions for discharges from upstream tributaries. The model was fitted to seven experts' estimates and historical measurements using Bayesian inference. Results were fitted only to the measurements were solely informative for more frequent events, while fitting only to the expert estimates reduced uncertainty solely for extremes. Combining both historical observations and estimates of extremes provided the most plausible results. The classical model reduced the uncertainty by appointing the most weight to the two most accurate experts, based on their estimates of less extreme discharges. The study demonstrates that with the presented Bayesian approach that combines historical data and expert-informed priors, a group of hydrological experts can provide plausible estimates for discharges and potentially also other (hydrological) extremes with relatively manageable effort.@en

The Netherlands has traditionally focused on managing flood risk. However, the frequent occurrence of droughts in recent years has brought attention to managing both extremes. Transitions between these opposite extremes pose additional challenges to water management, requiring a trade-off between water storage during dry periods and flood control during wet periods. In this study, we develop a framework to define wet and dry meteorological events and study their transitions using timeseries of meteorological data namely, precipitation, temperature and potential evapotranspiration. The magnitudes of event characteristics are retained, which presents a different approach to the normalized climate indices (like the Standardized Precipitation Index) commonly used in literature. We apply this framework to the Dutch part of the Meuse River basin in northwestern Europe using climate observations between 1951 and 2022. Our analysis shows a statistically significant increase in the amount of water lost from potential evapotranspiration compared to water gained from precipitation between April and September of the water year and an increase in the length of this drying period over the past decades. Such trends in the drying period are related to variability in potential evapotranspiration caused by rising temperatures in the region, indicating the potential for increased water shortage in Spring and Summer due to future temperature increases. We also identify abrupt transitions between opposite extreme events where there is a lack of water at the end of the second event as meteorological situations that challenge water management due to overlapping impacts like flash flooding, less time for water storage, and reduced water availability. We see such conditions occur in 6% of the wet-dry transitions and 20% of the dry-wet transitions, highlighting meteorological scenarios to which the hydrological response of the catchment can be simulated to increase our understanding of the combined risk of floods and droughts.@en

Without taking additional measures, flooding is becoming more likely and intense in a changing climate, which causes large economic damage. Households and firms are directly impacted by physical flood damage, but further ripple effects on society occur through business disruptions. By using post-disaster survey data from the 2021 flood event in the Netherlands, this study adds to the literature on business interruption duration and losses after flooding. The current empirical literature on flood impacts on firms is often unable to distinguish separate effects for flooded and non-flooded firms and does not incorporate flood severity and the influence of risk reduction measures. Here, we use multivariate regression models to determine depth-duration functions that describe the relationship between flood hazard characteristics and business interruption duration. This relationship can be used to calibrate flood damage models that capture indirect firm impacts. The prediction of business interruption after flooding allows for differentiation in business interruption between firms within a flooded area, reducing the reliance of these macroeconomic models on restrictive assumptions. Our results indicate that a day of business interruption duration costs a firm on average 0.5 % of their annual revenue; an effect that is stronger for firms with a weaker connection to their region. Flood damage mitigation (FDM) measures taken at the building level do not significantly affect business interruption duration, although further research on this is required. Finally, quick damage compensation is found to reduce business interruption duration and thus revenue losses, calling for higher insurance uptake and rapid and streamlined post-disaster insurance and government compensation.@en

A system of dikes in flood-prone areas continuously requires measures to mitigate changes such as ageing and climate change. Planning costly measures requires proper insight into system risk effects. Especially in a riverine dike system, the risk contributions of individual assets to the system flood risks are not independent, because reinforcement of a dike upstream increases the risks downstream. Tactical plans define the planning of consecutive measures to implement a flood risk reduction strategy, which may take decades. They may differ due to choices such as a prioritization metric, planning conditions and budget. In this study, a method is developed to compare different tactics to prioritize and plan measures in interdependent systems of dikes to reduce risks most effectively and efficiently. A case study meant as a proof of concept was carried out for the reinforcement of about 500 km of dikes along the Rhine River branches in the Netherlands. We studied the effects of 12 different tactical plans on the aggregated risks over time. The economic risks differ by up to about 40%, and the risks on victims differ by up to 70 %. We conclude that tactical planning and corresponding decisions are important for reduction of time-aggregated flood risks.

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This study provides an overview of the impact of the 2021 Summer floods in the Netherlands and the assessment of the effectiveness of various adaptation measures, evacuation strategies, and their impact on society. The floods were characterized by record rainfall in the cross-border region of the Meuse and Rhine basins and resulted in devastating losses in the Netherlands, Germany and Belgium. The study reports on a household survey conducted with 1,509 households in the wake of the 2021 flood event in the southern part of the Netherlands (province of Limburg). Using a descriptive approach, we present household experiences during several stages of the disaster management cycle, reporting on experienced flood hazard and impacts, evacuation, flood damage mitigation measures, the compensation progress, risk perceptions, and stress. Our findings highlight the role of early warnings and flood risk information provision in flood risk management. Risk perceptions influence both adaptation and evacuation behavior, as respondents who were aware of flood risks beforehand took significantly more flood damage mitigation measures compared with those who were not aware. Flood damage mitigation measures, such as building with water-resistant materials and elevating valuables, reduced flood damage by 20% to 50%. Our survey shows that of those who received warnings, the majority actually evacuated. However, residents not aware of any evacuation advice evacuated significantly less. Additionally, the majority (75%) of respondents experienced high or very high stress during and after the flood, which is most likely related to the destructive flood impacts and the slow and uncertain compensation experienced by many respondents. This paper describes the flood event and its consequences to provide insights into Dutch disaster management and what can be learned for potential future disasters in other contexts.@en

Flood events are expected to increase in their frequency and severity, which results in higher flood risk without additional adaptation measures. The information gained from flood risk models is essential in effective disaster risk management. However, vulnerability estimations are often a large driver of uncertainty, and flood damage is rarely estimated due to a lack of empirical damage data from flood events. This study uses a unique data set with experienced damages and the implementation of flood damage mitigation (FDM) measures on the household level, collected after the flood event in the Netherlands in 2021. Flood damage models that control for several hazard, exposure, and vulnerability indicators are estimated and allow for additional input in flood risk models. Previous estimates of the effectiveness of FDM measures are prone to a selection bias, as households that do, and do not implement FDM measures systematically differ in their risk profiles. By using an instrumental variable-estimation, this study overcomes this selection bias and finds significant reductions in flood damage due to FDM measures. These reductions can be incorporated in multivariate flood vulnerability estimations, which indicate that FDM measures significantly reduce flood damage. Providing information on flood hazard, as well as implementing early warning systems, is crucial for ensuring effective flood risk management.

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Structural reliability analysis often considers failure mechanisms as correlated but non-interacting processes. Interacting failure mechanisms affect each others performance, and thereby the system reliability. We describe such interactions in the context of flood defenses, and analyze under which conditions such interactions have a large impact on reliability using a Monte Carlo-based quantification method. We provide simple examples and an application to levee failure due to landward slope instability and backward erosion piping (BEP). The examples show that the largest interaction effects are expected when the trigger mechanism is relatively likely to occur and the affected mechanism has a relatively large contribution to the system reliability. For the studied levee example, interactions between slope instability and BEP increased the failure probability up to a factor 4. Implications for the assessment and design of flood defenses are discussed.@en

The condition of flood defence revetments is influenced by many different degradation processes such as animal burrowing, rutting and growth of weeds. Many of these processes are shock-based rather than progressive continuous. As shocks can cause a drop in performance, this means that the condition of a revetment can suddenly decrease, meaning that revetments can have significant initial damage at the beginning of a storm. Combined with the limited detection probability of common visual inspections of flood defences, this can have a significant influence on the reliability of flood defence systems, something typically not considered in reliability analysis. In this paper we study the reliability of a flood defence system subject to shock-based degradation. Various maintenance concepts are compared for a case study of a riverine flood defence of 20 kilometres length. This demonstrates that the current maintenance concept is insufficient to satisfy the reliability requirements for failure of the revetment. Overall, the joint influence of degradation and the existing maintenance concept leads to a 20 times higher failure probability estimate compared to a typical assessment without these aspects. Next, we demonstrate that both additional inspections, and targeted interventions to reduce the impact of for instance animal burrowing, can significantly reduce total cost and improve robustness of the considered flood defence system.

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The floods in the Netherlands in the summer of 2021 led to severe economic damage and losses in the affected area. A first estimate in September 2021 showed that more than 2,500 houses, more than 5,000 inhabitants and around 600 businesses were affected. Using the Dutch standard Flood Damage and Loss Model (SSM2017), and based on figures from international literature, the total damage in the Netherlands is estimated in the order of € 350 – 600 million. Physical damage to houses and businesses, business interruption, damage to infrastructure and crop losses were the most substantial. The differences in damage to individual structures (residential and commercial) were large. The estimated damage in the affected area clearly exceeds the damage of the Meuse River floods in 1993 and 1995 which occurred in the same region (converted to 2021 prices: around € 200 million and € 125 million, respectively, excluding damage due to business interruption). It is important to note that the largest damages and losses in 2021 occurred in the smaller regional rivers, mainly in the Geul floodplain, while in 1993 and 1995 most damage and losses were recorded in the Meuse floodplain.@en

The Wettelijk Beoordelingsinstrumentarium (WBI) is the legal set of instruments for flood risk analysis in the Netherlands. Often, engineers have the impression that some failure probabilities of flood defenses resulting from these instruments are overestimated. In an effort to better estimate the failure probabilities of dikes along the Dutch river Rhine, this study sets out to assess them with experts and compare them to model results. We used Cooke's method for combining experts’ estimates in a structured way and follow two approaches to estimate a system failure probability. In the first approach, experts estimate discharges that lead to at least one dike failure. This gives plausible results; failure probabilities between 1/30 and 1/17.000 in a year. The second approach is based on adjusting existing model-based assessment results, by estimating the model-bias and incorporating additional dependencies. This mostly leads to large, implausible, failure probabilities: Experts tend to give more conservative answers as they are asked for detailed estimates without clear reference values. This results in large uncertainty and consequently (too) high failure probabilities. Our research shows that when applied in a clear frame of reference, structured expert judgments can be successfully used for estimating the reliability of Dutch flood defenses.

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Risk-informed decision-making needs methods for assessing flood risk, and often the flooding probability and the consequences of floods (such as economic damage and fatalities) play an important role in the risk assessment. Also, measures to reduce the flood risk need to be formulated, in order to make a risk-informed decision, whether to accept the risk or to implement measures to reduce or to transfer the risk. These measures can be technical (for example, storm surge barriers) but can also be in the area of spatial planning or crises management. The outcome of such a process might be formalized in a “safety standards,” which can be used for the design of measures. These standards show remarkable differences between the United States, the United Kingdom, and the Netherlands.

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Dikes are an effective flood risk reduction measure in deltaic areas. Present risk analyses consist often of decoupled calculations of probabilities of dike failure and calculation of consequences of flooding given dike failure. However, the flood defense design determines not only the probability of failure, but influences the consequences of flooding as well. Especially when the dike has a ductile failure and breach growth behavior, due to a structural robust design, the consequences of flooding reduce. In this article, we present a novel assessment of risks and investments, valuing structural robustness of a construction type, represented by its ductile behavior during high loads. Therefore, the consecutive occurrence of initial dike failure mechanisms, failure path development, breach growth, and consequences is modeled integral and time-dependent. The investments consist of the costs to reinforce or reconstruct the flood defense to behave relatively ductile. This integral assessment enables to compare flood impacts of different construction types and different dimensions of designs. We applied it on a case in a riverine area in the Netherlands. The results show that the total societal costs and the individual risks on victims are very dependent on the construction type. The risk profile of a polder protected by a brittle or a ductile dike differs significantly. The brittle sand dike in the case requires larger dimensions than the more ductile dike with a clay core.

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Flood prone areas are often protected against flooding by an extensive network of flood defenses. To ensure their structural integrity, these flood defenses are periodically assessed. Many levees have been functioning well for decades, and have survived several relatively high hydraulic loads within their lifetime. However, information on survived load conditions is seldom included in levee safety assessments. Observed degradation from levee inspections is also not taken into account. That way, information that is useful to improve the accuracy of estimations of the actual strength of the levee remains unexploited. This study proposes a pragmatic approach to include observations of survived loads and levee degradation in the levee safety assessment. This approach consists of three steps: (1) a prior estimation of the failure probability, based on levee characteristics, (2) a posterior estimation of the failure probability, based on observed hydraulic loads, and (3) correction of the posterior failure probability estimation, based on levee inspections. In a case study, the estimated failure probabilities using this approach were much lower than when information on levee performance was not included. This study demonstrates the value of levee performance observations and how they could be included to improve levee safety assessments.

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Climate change and deterioration require a continuous effort to reinforce flood defences and meet reliability requirements. To efficiently upgrade flood defence systems, insight in costs and benefits of measures at a system level is required throughout the process of planning and design. Due to the size of flood defence systems the number of possible decisions is large, which hampers system optimization. We describe a greedy search algorithm that can find (near-)optimal combinations of reinforcement measures for dike segments. The algorithm has been validated by comparing results for 2800 different dike segments to an integer programming implementation. The difference in objective value (Total Cost) is only 0.04% on average, which is small compared to other uncertainties in assessment and design of dike segments. The algorithm is applied to a reinforcement project for a dike segment of 41 independent sections, and compared to the common design practice which uses reliability-based requirements on a section level. It is found that the resulting reinforced dike segment is 42% cheaper to construct than the one obtained from the common approach, based on the same input information. This illustrates the practical and societal value of the design approach using a greedy search algorithm in this context.

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Backward erosion piping is an internal erosion process, which compromises the stability of water retaining structures such as dams and levees. In this paper, we propose a numerical solution that combines a 2D Darcy groundwater solution with Exner's 1D sediment transport mass conservation equation. As an estimate of sediment transport, we tested four different empirical transport equations for laminar flow. The model performance was evaluated based on the results of the real-scale IJkdijk experiment. Through this, we were able to demonstrate the applicability of existing sediment transport equations to the description of particle motion during piping erosion. The proposed transient piping model not only predicts the pipe progression in time, it also allows for an identification of pore pressure transitions due to the erosion process. A major conclusion of the study is that from the four different modeling approaches for laminar flow, it is recommended to follow the approach of Yalin et al. regarding the simulation of backward erosion piping for dike configurations similar to those of the IJkdijk experiment.

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