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D2) Time dependency and interactions

Start: 09/2017
End: 03/2022
Status: Active

Contact details

Joost Pol

Delft University of Technology


The project focuses on two aspects of the new definition of safety standards as flooding probability. The first aspect is related to piping and accounts for most of the results, which show how time-dependent pipe development affects dike reliability. To this extend, we performed lab experiments, developed a pipe progression model, and integrated this knowledge into a time-dependent piping reliability analysis. Our analysis shows that dike reliability increases significantly in relatively short high-water durations or effective flood fighting. The second aspect explored the potential impact of interactions between failure mechanisms.

Figure 1 - Top: The Waal river dike at Beuningen during the 1993 flood (source: Rijkswaterstaat / Bart van Eyck). Bottom: Piping in the laboratory (source: Sam Rentmeester Fotografie with limited use due to copyrights) and the field (Photo by Joost Pool).

Motivation and practical challenge

It is of great societal importance to improve safety estimates to optimise investments. Current safety assessments result in unexpected high failure probabilities for some failure mechanisms, such as piping. These conservative estimates for the probability of failure may result in high costs for dike reinforcement projects in the Netherlands. In the case of high water levels (Figure 1, top photo), including the flood duration in the analyses is one of the aspects that can contribute to lower assessed failure probabilities and more efficient reinforcements.
Related to piping, the dike failure starts when water flowing through a sandy dike foundation erodes so much sand that it forms a small (mm size) channel or ‘pipe’ (Figure 2, innovative components). Therefore, an important challenge is the interpretation of field observations during floods. For example, sand boils are the only visual manifestation of piping, but most do not result in a dike breach. A better understanding of the erosion process in the laboratory and the field (Figure 1, bottom photos) is important to estimate the likelihood of a dike breach during a flood to plan emergency responses.

Research challenge

The research aims to show how to quantify failure probabilities, including (uncertain) flood durations and time-dependent failure processes. The assessment framework is elaborated for piping, for which a model shows the development over time.

Innovative components

Including time-dependent information in dike safety assessments requires understanding the development of failure mechanisms such as piping at different levels over several flood events. To do so, I use the following innovative components:

  1. A better understanding of the development of the piping erosion process over time, using small scale and large scale experiments.
  2. Modelling of the piping erosion process for deriving a simplified model that complements the current practice (Sellmeijer model).
  3. Exploring when interactions (causal dependencies) between failure mechanisms are relevant.

Based on this improved understanding, I am developing a probabilistic framework to integrate uncertainties and time aspects in hydraulic loads, dike properties and failure processes, both over single and several flood events. The framework quantifies the effect of time dependence in several types of water systems such as rivers, coasts, and lakes. The project focuses on piping failure, but similar probabilistic methods can be used for other failure mechanisms.

Figure 2 – Left. Piping schemes adapted from van Beek (2015) and dike reliability graphs sketched by Joost Pool.

Figure 2 – Right. Main components of the research (Photo on the lab by Sam Rentmeester Fotografie with limited use due to copyrights. Other photos by Joost Pool).

Relevant for whom and where?

Technical managers of flood defences, especially in areas with short flood durations. They can use the research to improve reliability estimates in assessment, design and operational phases. The research can also help in the planning of emergency measures.

Findings of this research are developed in the laboratory and a field test site and will be applicable to dike reinforcement projects in the Netherlands.

Progress and practical application

At the moment of writing (December 2021), the analysis of the experiments is finished. In the following months, the pipe erosion modelling and reliability analysis will be fine-tuned and applied to field-scale examples. The results so far indicate that a time-dependent analysis can considerably reduce calculated piping failure probabilities. The time-dependent analysis can decrease the probability of piping failure with several orders of magnitude in areas with short, storm-dominated floods. This effect is smaller in prolonged river floods but still significant if combined with timely flood-fighting interventions. Results also show that a breach often occurs after the flood peak. Reaching this peak can take several days in riverine areas, which is a significant delay for allowing operational flood management. The results can be applied in tailored dike reliability analysis and used to derive simplified rules for assessing time-dependent pipe development.

Recommendations for practice

  • Safety assessments and reinforcement projects should consider where they can benefit from the time required for piping development.
  • Discuss including flood-fighting interventions in reliability analyses; this yields lower failure probabilities and more efficient designs combined with slow pipe development.
  • Derive simplified rules for the assessment of time-dependent pipe development.
  • Keep investing in experimental research to study the piping process.
  • When using a failure path analysis to quantify residual strength, check for potential interactions between failure mechanisms, decreasing the reliability.

Last modified: 27/12/2021

Main researcher

Joost Pol

Delft University of Technology


Wim Kanning

Delft University of Technology Bas Jonkman

Delft University of Technology Matthijs Kok

Delft University of Technology

Contributing partners

Increased flood safety due to time-dependent pipe growth

Dike safety assessments can be optimised when considering the time that the water flowing underneath the dike takes to erode its foundation.

Joost Pol

Delft University of Technology

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Project outputs

Progression Rate of Backward Erosion Piping: Small Scale Experiments

Series of experiments with detailed pipe flow measurements to better understand the piping erosion mechanism.


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Bevat: Conference proceedings

Shields-Darcy piping-model. Verschil-analyse met Sellmeijer en D-GeoFlow

Analysis into the differences between the Sellmeijer rule and the Shields-Darcy for piping, focusing on model assumptions and scale effects.


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Bevat: Report

Progression rate of backward erosion piping in laboratory experiments and reliability analysis

Statistical analysis of pipe growth rates in existing lab tests, and a study of the potential of including time-dependent pipe growth in fail-ure probability analysis of dikes.


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Bevat: Conference proceedings

Temporal Development of Backward Erosion Piping in a Large-Scale Experiment

Monitoring the development of piping in a test dike on a large scale, for better estimation of time to failure and to validate piping models.

02/02/2021 by Joost Pol et al.

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Bevat: Publication open access journal



Reflection: Risk-based inspection and interactions between failure mechanisms

Safety standards of flood defences are based on probabilities of flooding. Using a variety of failure models and statistical methods, we try to assess these probabilities as good as possible, in order to take effective measures for flood risk reduction. The question is how well we actually have insight into the flooding probability, and whether we take all relevant factors into account.

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Reflection: The biggest flood risk in the rivers - bifurcation points or piping?

Flood risk along the Rhine branches: Flood risks along the major rivers continuously demand our attention. During this All-Risk webinar, we called attention to new research on the role of two of the mechanisms that influence flood risk: the two main bifurcations of the Rhine branches and the role of the failure mechanism piping. Can it be plausibly argued that one of the two causes are dominant?

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High water in Limburg during the summer 2021

11/10/2021 by Bas Jonkman

Commissioned by the Dutch Expertise Network for Flood Protection (ENW), a broad consortium of knowledge institutions, led by Delft University of Technology and Deltares,...

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