This study investigates how hydraulic and meteorological variables act together to affect dike stability, with emphasis on inner-slope failure during extreme hydrometeorological events. The variables influencing dike stability are first identified through a literature review, after which their correlations are examined and analysed using copula theory. The effect of these correlations is then assessed in more detail by applying a groundwater model developed with Pastas and performing slope stability calculations using the Bishop method.
The analysis focuses on the period from December 2023 to January 2024, when the Netherlands experienced high cumulative rainfall, elevated river discharges, and restricted outflow due to sea storm surges, leading to prolonged high water levels in the IJsselmeer–Markermeer system. The case study is a lakeside dike along Markermeer between Hoorn and Enkhuizen (about 17.8 km), where data availability enables detailed hydrological and geotechnical modelling. Two cross-sections (raai_2 and raai_3) are instrumented with multiple observation wells from phreatic to deep sand layers. Inputs combine hourly lake levels from Krabbersgat Zuid and the nearby Drieban pumping station, hourly precipitation and daily evapotranspiration from Berkhout station, and local groundwater measurements from 10 Nov 2023 to 25 Feb 2025. These data are used to calibrate and validate Pastas groundwater models and to evaluate slope stability for representative hydraulic loading conditions.
The literature indicates that phreatic levels around Markermeer and IJsselmeer are governed by external hydraulic loads, climate, internal soil properties, dike geometry, and local lake dynamics. Using statistical analysis, copula modelling, and time-series groundwater simulations, this study examines how precipitation and lake level jointly influence the phreatic surface within the dike. Results show a moderate positive correlation between cumulative local precipitation and lake water levels. Copula models, particularly the BB8 family, capture asymmetric dependence between rainfall and water level, highlighting an increased likelihood of joint extremes.
For stability evaluation, observed groundwater data were first used as input to D-Stability to compute the factor of safety (FoS) over selected periods. This “dependent” case reflects the real, correlated relationship between precipitation and water level and shows a moderate negative correlation with FoS, meaning increases in either driver reduce stability. An “independent” case is then constructed by generating a new water-level series from the fitted bivariate copula using conditional sampling with rank-exact back-mapping, so that water level is statistically independent of precipitation while preserving the marginal (univariate) distributions. The Pastas model is re-fitted with this synthetic water-level series to produce new groundwater heads, and FoS is recomputed. Under the observed (dependent) case, peak external water levels coincided with prolonged high precipitation, producing higher phreatic levels and a lower minimum FoS (1.745). When the same marginals were used but the drivers were made independent, peak water levels were lower and the minimum FoS improved (1.768). By evaluating the correlation, the dependent case shows stronger negative correlation for both precipitation (-0.67) and water level (-0.49) versus FoS. In the case of independent variable, the correlation between water level and FoS strengthened to −0.85, while the correlation between precipitation and FoS weakened to −0.18.
Based on the previous results, it can be concluded that during the wet season, the correlation between precipitation and water level leads to a more conservative outcome, expressed as a lower factor of safety (FoS) for dike stability. This finding is consistent with real-world conditions, where periods of higher rainfall typically occur together with higher local lake water levels caused by runoff from around the lake, direct rainfall itself, and polder drainage pumping into the lake. This conclusion is based on the assumption that the water level dataset used in this study represents local water level observations, where in reality the actual local water level at this specific dike section may differ slightly depending on wind magnitude and direction. The main recommendation for dike assessment based on this study is that the correlation between precipitation and water level should be explicitly considered in stability analyses, since neglecting this dependence may underestimate phreatic levels within the dike and result in a less conservative estimate of the factor of safety.