Backward erosion piping (BEP) is a failure mechanism of hydraulic structures like dams and levees on cohesionless foundations subjected to seepage flows. This article models the time-dependent development of BEP using numerical simulation of the erosion process. A 3-dimensional finite element equilibrium BEP model is extended with a formulation for the sediment transport rate. The model is compared to and calibrated with small- and large-scale experiments. Finally, a large set of simulations is analyzed to study the effects of factors such as grain size, scale (seepage length) and overloading on the rate of pipe progression. The results show that the development of BEP in the small-scale experiments is predicted well. Challenges remain for the prediction at larger scales, as calibration and validation is hard due to limited large-scale experiments with sufficiently accurate measurements. The results show that the progression rate increases with grain size and degree of overloading and decreases with seepage length, which is consistent with experimental observations. The model results provide a better physical basis for incorporating time-dependent development in the risk assessment and design of levees.

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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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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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This study introduces a method for assessing the annual failure rate of levees based on information from historical floods, while also considering the return period of these past events. Also, an approach has been developed to quantify the influence of deviating conditions on failure rates. The presence of deviating conditions at failed and survived levee sections is analyzed based on satellite observations. Bayesian techniques and likelihood ratios are used to update the failure rate as a function of the presence of deviations. The river system of Sachsen-Anhalt, Germany, is used as a case study. It experienced severe floods with many levee failures in the years 2002 and 2013. It is found that the presence of geological deviations had a significant influence on the observed failure rate and that failure rate increases with the magnitude of the hydraulic loading. It is also discussed how the expected number of failures in a system during a flood event with a certain magnitude can be estimated. The results of this study can be used to further optimize soil investigations, calibrate the results of more advanced reliability analyses and complement risk assessments, particularly in data-poor environments.

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Backward erosion piping (BEP) is a form of internal erosion which can lead to failure of levees and dams. Most research focused on the critical head difference at which piping failure occurs. Two aspects have received less attention, namely (1) the temporal evolution of piping and (2) the local hydraulic conditions in the pipe and at the pipe tip. We present small-scale experiments with local pressure measurements in the pipe during equilibrium and pipe progression for different sands and degrees of hydraulic loading. The experiments confirm a positive relation between progression rate and grain size as well as the degree of hydraulic overloading. Furthermore, the analysis of local hydraulic conditions shows that the rate of BEP progression can be better explained by the bed shear stress and sediment transport in the pipe than by the seepage velocity at the pipe tip. The experiments show how different processes contribute to the piping process and these insights provide a first empirical basis for modeling pipe development using coupled seepage-sediment transport equations.

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The Netherlands is protected against major floods by a system of primary flood defenses (levees, dunes and hydraulic structures). These must comply with standards defined in terms of maximum allowable probabilities of flooding. Therefore, a new assessment framework for the main failure mechanisms is based on a probabilistic approach. One of the failure mechanisms which is not yet following such a probabilistic approach is instability of the outer slope of a levee. This failure mechanism is of importance after a rapid water level drop after a high-water event. In such an event, the pore water pressures in the levee are still high, and if an instability happens flooding can occur when (1) there is no time to take emergency measures before a second high-water event follows and (2) there is insufficient residual strength to prevent flooding during this consecutive high-water event. Levee reinforcement projects in the Netherlands allocate significant resources to resolve the presumed lack of safety of the levee due to the outer slope instability mechanism. Hence, this paper discusses how outer slope stability safety can be assessed probabilistically. A failure due to outer slope instability depends, besides the characteristics of the levee, on the peak water level, the water level drop velocity, the inter-arrival time between two consecutive high-water events and the time needed to take emergency measures. In this paper, a framework based on event trees is presented, using Intensity-Duration-Frequency-curves to include the time dependent statistics of the water level drop. This is a novel approach for outer slope instability in the Netherlands and results in less conservatism in assessments and designs, and therefore less required resources to mitigate the mechanism.@en

Prioritisation of flood defence maintenance is typically based on visual inspection. However, literature shows that the Probability of Detection (PoD) of visual inspection can vary significantly. Here we investigate the PoD for visual inspections of flood defence structures, the consistency of damage classification, and the influence of different variables on the PoD, such as past experience. Four flood defence sections were inspected by 22 different inspectors for a variety of damage types, such as animal burrowing and damage to block revetments. It is found that the PoD varies significantly both per damage type and inspector. Additionally, the estimated severity of damages varies significantly in comparison to the reference situation: over half of the registered damages is assigned a different severity compared to the reference, which potentially leads to incorrect maintenance measures. A likely explanation for the variation in results is the complexity of inspection guidelines and task definitions. Therefore it is advised to simplify inspection guidelines and use more focussed inspections for the most important types of damage. This likely leads to both a reduction of the number of false negatives associated with an increase in flood risk, and better risk-based asset management and maintenance prioritisation in general.

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Parameter determination is the first step in geotechnical engineering. Engineers are often confronted with limited data, large variations and different types of tests, both in-situ and laboratory tests. Within this complex setting, Codes require cautious estimates, so called characteristic values, preferable substantiated with observations and statistical methods. In this study, these statistical methods for populations and trend-functions are elaborated. Most codes and standards only refer to population statistics, whereas the reality is that, with the use of CPTs, trend functions such as correlations or transformation functions are more relevant. The aim of this paper is to provide a method how to use CPT and laboratory tests in practice in order to calculate characteristic values, on the basis of pairwise established CPT-based correlations, typically applicable for line infrastructure projects such as levees. @en

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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This paper presents a large-scale backward erosion piping experiment aimed at studying the erosion rate. This temporal aspect of piping complements previous research that focused on the critical head. To study the progression rate in realistic conditions, an experiment was carried out on a 1.8 m high levee with a cohesive blanket on a sandy foundation. The pipe was guided along a row of pore pressure transducers in order to measure its temporal development. Pipe development in space and time was successfully derived from pore pressure changes, showing an average progression rate of 8  m/day during the progressive erosion phase. The results show a relation between upstream gradient and progression rate. Furthermore, analysis of the eroded sand mass shows a relatively large pipe volume compared to existing lab tests, and an approximately linear relation between pipe length and volume. The results and insights from this study can be used to validate and improve transient piping models, leading to more accurate dam and levee safety assessments.@en

Most research on backward erosion piping (BEP) focuses on the critical conditions leading to failure. This paper studies the development of piping over time once the critical conditions are exceeded, which is useful to estimate time to failure. A commonly used small scale rectangular box setup is modified in order to monitor pore pressures and pipe pressures with a high spatial and temporal resolution. The experimental program includes three different sand types to study the effects of grain size and compaction, and different degrees of hydraulic loading. The results indicate that the transport of particles in the pipe affects the progression rate, and that the progression rate is related to the bed shear stress in the pipe. @en

Hindcasting of past levee failures enhances insights in the performance and vulnerability of levees. The scarcity of field evidence makes identifying the cause(s) of failure difficult. Under these circumstances, multiple scenarios and model choices are possible to characterise and to model the failure. This paper shows how probabilistic Bayesian techniques advance the procedure of hindcasting of levee failures. In the developed approach, a-priori levee information, and failure observations are systematically taken into account to determine the most likely scenario and the most representative model choices to characterise the failure most accurately. Observations, such as the slip surface, are taken into account in the probability estimates. The levee failure near Breitenhagen, Germany (2013) is used as a case study. The levee failed during river floods due the instability of the landside slope. The levee failure was most likely triggered by locally weak soil conditions and unexpected high water pressures due a connection between a pond on the riverside of the levee and the aquifer. These conditions were likely caused by the occurrence of a previous breach at this location. The approach developed in this paper is expected to support a more systematic and objective method of analysis of other levee failures.

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Spatial variability and limited measurements often result in low reliability estimates of geotechnical failure modes of dikes (i.e., earthen flood defences). Required dike reinforcements are usually not executed within a few years after inception, which enables efforts to improve reliability estimates by reducing uncertainty. Often decision makers are unclear on whether uncertainty reduction is worth investing, and which (combination of) methods yields the highest Value of Information (VoI). This paper presents a framework to assess the VoI of two uncertainty reduction methods (proof loading and pore pressure monitoring) for a case study of a typical river dike with an insufficiently stable inner slope, using a decision tree. In all cases, a positive VoI was found for at least one strategy consisting of a proof load test, monitoring or both. The optimal strategy of proof loading and monitoring has a VoI of 4.0 M€, being a reduction in total cost of 25% compared to a conventional dike reinforcement. It was also found that sometimes proof loading enhances the VoI of pore pressure monitoring, which demonstrates the benefits of jointly considering different methods in a single decision tree. The decision framework yields insight in total cost and VoI of risk reduction strategies, which enables decision makers to determine where proof loading and/or pore pressure monitoring are efficient, leading to more efficient flood defence asset management.

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The Netherlands is protected against major floods by a system of primary flood defenses. These primary flood defenses have to comply with flood protection standards. Since 2017, these are defined in terms of maximum allowable probabilities of flooding. This is why a new set of tools and guidelines had to be developed, allowing for probabilistic as well as semi-probabilistic assessments. Semi-probabilistic assessments rest on a Load and Resistance Factor Design (LRFD) approach. Since major levee systems are essentially series systems with little to no redundancy, the difference between component and system reliability is essential for reliability analyses of flood defenses. This paper discusses the code calibration procedure that was developed to ensure consistency between probabilistic and semi-probabilistic assessments of flood protection systems and their components. Example applications are provided for two failure modes: slope instability and dune erosion. The newly calibrated semi-probabilistic rules allow practitioners to assess the reliability of flood protection systems on the basis of component-level semi-probabilistic LRFD analyses for individual failure modes.@en

Forensic analysis of past failures is valuable to improve our understanding of levee behavior. In this article a new systematic approach of forensic analysis for levee failures is proposed and applied to the Breitenhagen levee breach that occurred along the river Saale in Germany in 2013. The purpose of this study is to identify the cause of the breach based on the proposed approach, even though limited data is available. Based on the information prior, during and after the breach of the levee, a slope stability model is developed for the entire event. First, results from this model are obtained based on the expected values of the uncertain parameters and the best estimates of the situation. Uncertainty of the model is included in the calculation subsequently by defining possible failure scenarios. The most likely failure scenarios are derived from the data and included into the model so that it is possible to eliminate or validate all possible causes by means of a sensitivity calculation. It is concluded that the levee breach is likely caused by locally weak soil conditions, unexpected high water pressures due to a connection between a pond and the aquifer and unexpected saturation of the levee. These conditions are associated with the occurrence of a previous breach at this location.@en

Backward erosion piping is an important failure mode of dikes and dams. The time required for the backward erosion process to result in dike failure is expected to be an important factor in the safety of dikes. This holds especially in coastal and estuarine areas which are dominated by storm surge, and pipes may not fully develop during a storm. Furthermore, insight in the duration of the various piping stages can assist in developing effective emergency mitigation measures. However, the temporal development of piping is hardly studied quantitatively, as most experimental and modelling studies focus on the critical head. Also data of real breaches is generally insufficient to determine the time to failure. As a result, currently the contribution of time required for pipe growth cannot be quantified in a deterministic and reliability analysis. In this study, it is investigated how the pipe progression rate can be predicted and applied to dike reliability. The data analysis is based on a composition of 45 small, medium and large scale experiments from six studies. Advancement rates are related to the applied hydraulic gradient and soil properties using a multivariate analysis. From the analysis we derive an empirical model for the advancement rate, including a quantification of the uncertainty. This model is applied in a reliability analysis of a hypothetical coastal and riverine dike. The results of our analysis may be used to validate transient numerical piping models, perform time-dependent probabilistic dike safety analysis and support emergency response.@en

This paper presents a Bayesian model to determine the model uncertainty of a critical horizontal gradient model for piping for dikes, such a Lane and Bligh. A Bayesian model is needed for two reasons. First, there is a large overlap in cases that failed and survived. Second, the evidence of the failed cases is limited .The model consists of a non-informative prior that is combined with likelihood functions for failed and survived cases. This involves modeling the mean and standard deviation of the model uncertainty as random variables. For survived cases we know the limit state function was larger than 0 for the observed water level. For failed cases we know the limit state function was smaller than 0; or Z = 0; which is a less conservative assumption. This information is used to determine the likelihood functions for failed and survived cases. The prior and likelihoods are combined to find the posterior distributions of the mean and standard distribution of the model uncertainty. Using integration, this finally results in the (lognormal) distribution of the model uncertainty. The model is applied to the data of Bligh and Lane and shows both a high mean and high standard deviation of the model uncertainty, where the model of Lane performs better than Bligh. It is recommended to tailor the proposed model to dikes by making a different distinction between horizontal and vertical erosion. Furthermore, it is recommended to apply the model to more dike specific data since the Bligh data mainly consists of dams instead of dikes. @en