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.

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.

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.

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.

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.

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.

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.

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.

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.