The Random Material Point Method for assessment of residual dyke resistance

Abstract

Flood protection infrastructure requires constant investments to cover the increasing flood risk. However, due to over-conservatism in (dyke) safety assessments, poorly targeted investments can be made. Over-conservatism can be avoided by understanding the entire failure process, from the initiation of failure until flooding. Dyke slope instability is one of the main initiation mechanisms evaluated during a safety assessment. Following an initial instability, a slope failure occurs, where large deformations may occur as the failure mass slides along the failure surface. A large initial failure mechanism may immediately trigger flooding, but in most cases secondary mechanisms, such as new slope failures, are required to flood the hinterland. The dyke may have enough resistance to prevent secondary mechanisms and thereby prevent flooding. Therefore, dyke assessments can be optimised by assessing the potential for secondary failures.

The standard methods for dyke slope stability assessment cannot model large deformations. This thesis therefore develops and applies the Material Point Method (MPM), a large deformation variant of the Finite Element Method, to investigate the residual (remaining) resistance of a dyke against flooding after an initial slope instability. The residual dyke resistance has been assessed within a risk-based framework using the Random MPM (RMPM), which accounts for the effects of soil heterogeneity on the failure process by combining random fields with MPM. From the realisations of an RMPM analysis, both the probability of initial failure as well as the probability of flooding may be determined. Moreover, with RMPM, the likelihood of failure processes can be evaluated such that the process between initial failure and flooding can be understood.

To model the external water level in the RMPM analysis, the application of boundary conditions in MPM has first been investigated. The thesis shows that the boundary conditions should systematically match the MPM discretisation. Improvements of MPM, such as the Generalized Interpolation Material Point Method (GIMP), often change the discretisation. Therefore, the accurate application of a boundary condition can therefore depend on the version of MPM being used. Consistent boundary conditions are described in this work for MPM and GIMP. For standard MPM, a consistent boundary condition is proposed for simple 1D problems. However, it is shown that this solution is not generally applicable for dyke slope failures or other higher dimensional problems. For GIMP, two generally applicable algorithms for (almost) consistent boundary conditions are proposed: one algorithm constructs the exact material boundary, while the other merges the support domains of all material points. The algorithms are shown to outperform other boundary condition methods presented in literature.

The residual (dyke) resistance has been investigated by modelling both a 2D dyke failure and 3D slope instability using RMPM. It is shown that secondary failures (required to trigger flooding) often do not occur or may not be large enough to trigger flooding. Therefore, the probability of flooding can be significantly lower than the probability of an initial failure due to residual dyke resistance. In the best case scenario for the problem analysed, a reduction of the probability of flooding compared to the probability of initial failure of more than 90% has been observed, while in the worst case only a 10% reduction was found. The reduction was high (90%) for a material without layering of the spatial variability of the strength properties and decreased when the spatial variability was more layered. However, note that, to reduce computational costs, the probability of initial failure was unrealistically high in these examples, i.e. the dyke was relatively weak. In stronger slopes, secondary failures are less likely and more residual dyke resistance is therefore expected. Additionally, secondary slope failures are less likely in 3D simulations compared to 2D simulations, generally due to the additional resistance of the sides of the failure surfaces (the so-called 3D-effect). A 2D simulation can therefore be seen as a conservative estimate of the residual dyke resistance. In 3D, the failure process more often spreads sideways rather than backwards. This is also beneficial for dyke slope stability assessments, where backward failures are required to trigger flooding.

The degree of anisotropy of the soil heterogeneity changes the expected failure process. For smaller horizontal scales of fluctuation, i.e. less layering of the soil, secondary failures are less likely to occur, since the initial and secondary failures are mostly uncorrelated. Additionally, in the 3D simulation, smaller horizontal scales of fluctuation triggered small failure blocks, again likely to reduce the risk of flooding. For larger horizontal scales of fluctuation, initial failure in a weaker layer can more easily trigger secondary failures through the same layer, thereby decreasing residual dyke resistance. A depth trend, i.e. a linear increase with depth, in the mean resistance of the material, typical due to compaction processes, also impacts the failure process. For a material without a depth trend, progressive failure occurs along approximately circular failure surfaces, whereas for a material with a depth trend, a steady flow like behaviour along a gentle ’straight’ slope occurs. Moreover, retrogressive failure can flow in any direction for a material with a depth trend while avoiding local strong zones.

This thesis highlights that RMPM can provide estimates of the residual dyke resistance, thereby more accurately estimating the probability of flooding due to dyke slope instability in many situations. This leads to more targeted and cost effective dyke reinforcements. RMPM also provides insight into the size and shape of the initial and subsequent failures. RMPM can therefore be used in future research to develop guidelines for practice to approximate the probability of flooding, for example based on the probability and the shape of the initial failure computed with a small deformation model.