## Outcome

The current assessment of dike slope instability is limited to predicting the likelihood of the initial instability, as conventional methods can not predict the failure process beyond. This project has further developed the Material Point Method (MPM), which can evaluate the processes after an initial instability. Analyses of simple dike geometries with MPM have shown that a significant reduction in the calculated probability of flooding can occur by assessing the complete failure process. Moreover, the results show that secondary failures are more likely when the first failure occurs in a weak layer than a more homogeneous material.

**Figure 1.** Sequence of slope instabilities that lead to flooding (source: Photos by Grubert, P. (2013) and schemes adapted from Calle, E.O.F., Dijk doorbraak processen (2002), Figure 4.1).

### Motivation and practical challenge

The challenge of this project is to predict for which dikes slope instability can(not) be allowed, i.e. depending on whether it causes flooding. The failure process of slope instability starts with a crack in the crest or inner slope (**Figure 1, photo 1**). After the crack has developed, deformations start as the slope slides (**Figure 1, photo 2**). For dikes with residual resistance, these deformations may stop before flooding occurs, while for others, large deformations occur (**Figure 1, photo 3**) potentially leading to secondary slides., Flooding is unlikely to occur for some dikes even after very large deformations. For others, the deformation will lead to flooding due to a dike breach (**Figure 1, photo 4**). Allowing an initial slope instability for dikes with residual dike resistance may be possible when flooding is unlikely to occur, i.e. a dike breach is unlikely. Considering this residual resistance can lead to more efficient designs, especially for dikes with a large width. Dike reinforcement can then take place where it is most necessary. Modelling and understanding the failure process helps predict in which cases the failure process stops before flooding due to a dike breach. Thereby, we can help engineering expertise evaluate and expand the existing guidelines for dike slope instabilities.

### Research challenge

Implementing the new safety standards requires more realistic estimates of the probability of flooding. However, these realistic estimates are difficult as current assessment methods only predict failure initiation, not the failure process until flooding. Therefore, the challenge of this research was to design a method to predict the failure process and to use the method to determine the effect of residual dike resistance on the probability of flooding.

### Innovative components

To predict if a dike may breach after the initial slope instability, I developed and used the (Random) Material Point Method (R)MPM. MPM is a new modelling approach similar to the widely used Finite Element Method that allows us to model the start of the initial failure and the dike deformations that may follow. Thereby, I determine the residual dike resistance, which is the difference between the probability of slope instability and a dike breach (**Figure 2**).

The model is set up for a given dike section and accounts for the variability in the dike and subsoil properties by generating several possible realisations of the material properties, each equally likely to occur yet different. Due to the variability, the failure process may also be highly variable, and MPM is therefore expanded into a fully probabilistic tool (Random MPM). Thereby, I extend the current probabilistic framework for dike design to include residual dike resistance. RMPM computes for each realisation if initial instability and flooding occur. The probability of initial instability and flooding can be estimated from all these failure processes. Thereby, the residual dike resistance is estimated. Finally, the results are compared to the existing guidelines to provide insight into their applicability.

### Relevant for whom and where?

The research is relevant for anyone designing or assessing dikes who considers taking residual dike strength into account for dikes with a large width or dikes with a height above the water level.

*So far the research components are developed for typical dike sections in the Netherlands without a specific case study or location in the map.*

### Progress and practical application

Significant residual dike resistance was present in the examples tested, especially for wide dikes or lower water levels (compared to the dike height). In other words, MPM can reduce the calculated probability of flooding significantly compared to initial failure, reducing over-conservative calculations.

The dikes tested in the examples were relatively weak compared to realistic dikes. This condition ensured a relatively high probability of initial failure and saved on computation costs. Consequently, these examples had a relatively ‘low’ residual dike resistance compared to realistic examples. The benefit of using MPM can therefore be expected to be higher for more realistic examples.

The analysis showed that the reduction is highly dependent on the geometry, material properties, soil variability and river/sea water level. Current guidelines for residual dike resistance assume a ‘safe’ remaining dike geometry after the initial failure, which will never result in flooding. However, due to the large variation in outcomes after an initial failure, such a ‘safe’ geometry has not been found in the examples tested. In other words, the probability of flooding can be significantly reduced by residual dike resistance but will not become zero. For details about findings, see the related outputs.

### Recommendations for practice

- Evaluate failure processes up to flooding to reduce over conservatism.
- Be careful with quick estimations of the failure process.
- Provide detailed descriptions of dike slope failures for the development of MPM.
- Use MPM to model the failure process without replacing conventional methods for estimation of initial failure.
- Account for the effect of soil variability on slope instabilities as it leads to more efficient designs (with or without modelling the failure process).

Last modified: 27/12/2021

## Contributing researchers

Guido Remmerswaal

Delft University of Technology

### Project outputs

### Boundary conditions and dike reliability assessment using the Material Point Method (MPM)

By considering the residual dike strength, the computed reliability can increase compared to conventional assessments.

08/01/2019 by Guido Remmerswaal et al.

View detailsBevat: Conference proceedings

### An investigation of stress inaccuracies and proposed solution in the material point method (MPM)

Three modifications to MPM are implemented, and together these are able to remove almost all of the observed oscillations in the model.

14/11/2019 by Guido Remmerswaal et al.

View publicationBevat: Publication open access journal

### Evaluating residual dike resistance using the Random Material Point Method

The resistance against flooding after initial failure due to slope instability of an idealised dike reduces the probability of flooding by 25% with respect to the initial failure.

01/05/2021 by Guido Remmerswaal et al.

View publicationBevat: Publication open access journal

## Events

### 14/06/2021

Reflection: Macro stability - better parameters or models or do we need to reinforce the dikes?

Macro instability of the inner slope is an important failure mechanism that has a large influence on the costs of dike reinforcements and their impacts on the landscape. There are various uncertainties considering the strength parameters and models. There seem to be various options when a dike does not meet the standards: better parameter estimation, better models, or realize a conservative and expansive reinforcement. Which options could we explore to deal with macro instability in an efficient manner?