As the Material Point Method (MPM) uses both a mesh and a point discretisation scheme, the application of boundary conditions is difficult, currently limiting the flexibility of the method. While many boundary condition options have been used in the literature, the accuracy of Neumann boundary condition options has not yet been studied. Four options have here been evaluated for 1D and 2D benchmarks, although none of the options were found to be both accurate and generally applicable in MPM. However, for the generalised interpolation material point method (GIMP), the application of surface tractions on support domain boundaries or on a detected surface are valid options. Large differences between these two accurate options and the application of tractions at surface material points, a method regularly used in the literature, have been observed.

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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.@en

Structural reliability analysis often considers failure mechanisms as correlated but non-interacting processes. Interacting failure mechanisms affect each others performance, and thereby the system reliability. We describe such interactions in the context of flood defenses, and analyze under which conditions such interactions have a large impact on reliability using a Monte Carlo-based quantification method. We provide simple examples and an application to levee failure due to landward slope instability and backward erosion piping (BEP). The examples show that the largest interaction effects are expected when the trigger mechanism is relatively likely to occur and the affected mechanism has a relatively large contribution to the system reliability. For the studied levee example, interactions between slope instability and BEP increased the failure probability up to a factor 4. Implications for the assessment and design of flood defenses are discussed.@en

The material point method (MPM) shows promise for the simulation of large deformations in history-dependent materials such as soils. However, in general, it suffers from oscillations and inaccuracies due to its use of numerical integration and stress recovery at non-ideal locations. The development of a hydro-mechanical model, which does not suffer from oscillations is presented, including a number of benchmarks which prove its accuracy, robustness and numerical convergence. In this study, particular attention has been paid to the formulation of two-phase coupled material point method and the mitigation of volumetric locking caused numerical instability when using low-order finite elements for (nearly) incompressible problems. The numerical results show that the generalized interpolation material point (GIMP) method with selective reduced integration (SRI), patch recovery and composite material point method (CMPM) (named as GC-SRI-patch) is able to capture key processes such as pore pressure build-up and consolidation.@en

Due to a lack of large deformation dyke assessment models, primary failure mechanisms, such as inner slope failure, are often used as a proxy to assess the probability of failure of a dyke. However, a dyke continues to fulfil its main function unless, or until, flooding occurs. The Random Material Point Method (RMPM) is used here to investigate residual dyke resistance, which is the resistance against flooding after initial failure. RMPM combines random fields with MPM in a Monte Carlo simulation and has been extended here to include the effects of an external hydrostatic pressure on a dyke’s outer slope. The residual resistance of an idealised dyke (computed using RMPM) is shown to reduce the probability of flooding by 25% with respect to the initial failure. A lower degree of anisotropy of the spatial variability increases the residual dyke resistance. RMPM simulates, as expected, a lower residual dyke resistance for larger initial failures and/or a higher water level. A ‘safe’ remaining geometry has not been found, since even small initial failures can result in an unacceptable probability of flooding, highlighting the importance of modelling the entire failure process.@en

The material point method (MPM) is used to model both rotational and horizontal sliding failure mechanisms of dykes under external (water) loading. To model the different failure mechanisms, an external hydrostatic water pressure has been applied on the canal side of the dyke by applying a newly developed boundary condition. The boundary condition detects the material boundary and distributes the applied load to the nodes of the background mesh. The definition of dyke failure has also been investigated using MPM. In conventional dyke assessment, using (for example) the finite element method (FEM), the dyke is considered to have failed as soon as an initial failure occurs. However, the dyke may still be able to resist the flow of water, and this continuing ability to resist water flow is known as residual dyke strength. By taking account of residual dyke strength, for example with MPM as shown in this paper, the computed reliability can increase compared to conventional assessment, as in some cases total dyke failure does not occur after an initial slope failure. Finally, spatial variability is considered using the random material point method (RMPM), which combines random fields with MPM in a Monte Carlo framework. When considering spatial variability, a significant gain in reliability due to residual dyke strength has been observed, but further investigation is required to fully understand the effect of spatial variability on residual dyke strength. In order to simplify this preliminary investigation, the adopted soil properties in this paper have not been based on actual soils used in dyke construction; the results are only intended to indicate the capabilities of RMPM and develop hypotheses on the effect of residual dyke strength.@en

Stress inaccuracies (oscillations) are one of the main problems in the material point method (MPM), especially when advanced constitutive models are used. The origins of such oscillations are a combination of poor force and stiffness integration, stress recovery inaccuracies, and cell crossing problems. These are caused mainly by the use of shape function gradients and the use of material points for integration in MPM.The most common techniques developed to reduce stress oscillations consider adapting the shape function gradients so that they are continuous at the nodes. These techniques improve MPM, but problems remain, particularly in two and three dimensional cases. In this paper, the stress inaccuracies are investigated in detail, with particular reference to an implicit time integration scheme. Three modifications to MPM are implemented, and together these are able to remove almost all of the observed oscillations.

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This paper describes current work on the implementation of non-trivial boundary conditions (BCs) for improving the general applicability of the Material Point Method (MPM) to geotechnical boundary values problems. It summarises novel boundary treatments (non-trivial BCs) in MPM for (i) flow conditions, as well as (ii) the application of a surface traction on a moving boundary for solid materials. Both treatments are required, for example, to estimate the consequence of slope failure in geotechnical engineering. the flow condition BCs have been used to stimulate a subcritical flow and the surface traction BC has been applied on top of aslope leading to failure. Both examples show that these new treatments are useful in solving practical problems.@en

This paper investigates embankment reliability based on the ultimate limit state (ULS). The ULS is generally not clearly defined and, especially for flood defences, the ULS is currently under discussion. According to Dutch law [1], flooding which leads to either casualties or substantial financial damage is considered as the ultimate limit state of a flood defence structure. However, initial slope instability is regarded as flood defence failure according to guidelines for the assessment of macro-instability of dykes [2]. Allowing initial failure, but preventing a dyke breach, is not prohibited by the current Dutch regulations and can lead to more efficient design. Analysis of both large deformations as well as the influence of spatial variability of soil properties is important to assess the reliability of a dyke against breaching. This paper uses a new technique called the random material point method (RMPM) [3], which combines MPM [4] for modelling large deformations, with random fields [5] for modelling soil variability, in a Monte Carlo simulation.@en