Spatial variability in dike stability assessments

Abstract

The safety of the Dutch dikes depends on various failure mechanisms. Macro stability, a geotechnical failure mechanism, is highly affected by differences in soil strength because the sliding plane propagates through areas of least resistance. The variations in soil properties in space, also known as spatial
variability, are caused by geological processes and determine the locations of weaker zones in a dike. This highlights the importance of incorporating spatial variability into dike stability assessments.

The approach to incorporate spatial variability in the official Dutch assessment framework (WBI2017) relies on various assumptions. It assumes complete local variance reduction and neglects that the failure mechanism propagates through the weaker zones, leading to a mean strength reduction. Moreover, it assumes a default value for the ratio between local and regional variance α = 0.75, which lacks empirical evidence. Another method to incorporate spatial variability in stability calculations is the Random Finite Element Method (RFEM). This probabilistic technique models strong and weak zones through random fields. However, the main drawback is its considerable computation time, making it impractical to use for the assessment of the hundreds of kilometers of dikes in the Netherlands.

To address these issues, this research answers the question: What is an effective approach for incorporating spatial variability in soil into dike stability calculations? The study is divided into two parts: a data analysis and the creation of an RFEM model.

The first part investigated national and regional spatial correlations using variograms. The study found that the local spatial variance cannot be analyzed with variograms based on the national dataset. This is because the variograms average the variance in the local data due to their large scale. Investigating
local variability requires local data with a high enough density and accuracy in the research area.

In the second part, the inclusion of spatial variability was studied for a case study dike using RFEM, which is part of dike trajectory 34-2, located between Willemstad and Noordschans. The research highlighted two differences between assumptions made by RFEM and the WBI2017 method: (1) the
inclusion of statistical uncertainty and (2) the use of different stress components in calculating the undrained shear stress. The results of the different methods can only be compared if these differences are accounted for. Furthermore, the study found that using a probabilistic calculation with α = 0.8 better fits the results of the realistic RFEM model of the case study dike, particularly in the lower tail of the distribution of the results, compared to the default value of α = 0.75. Therefore, it can be concluded that α = 0.8 leads to a more realistic approximation of the probability of failure of this cross-section.

To investigate the importance of this finding, an assessment was carried out following the guidelines of WBI2017 but with α = 0.8. This showed that the probability of failure for dike trajectory 34-2 was reduced by 39.72% but that the safety category of the dike trajectory (for macro stability) remains unchanged.

Therefore, the answer to the research question is that when considering the computational requirements of RFEM, it is more effective to keep using the WBI2017 approach of implementing spatial variability into the input parameters of dike stability calculations with α = 0.75.

These findings are relevant as they validate the use of the current method with the available data. The study used different approaches for incorporating spatial variability in stability calculations and provides valuable insights for future research.