One of the main challenges in dike design in the Netherlands is to guarantee a sufficient safety level against the development of macro-instabilities in a dike. A case study was performed on a dike section at Herrewijnen-Opijnen, which is part of the Heesseltse Uiterwaarden in the Dutch province of Gelderland. The dike located at this site no longer fulfils the required safety standards, and therefore dike reinforcement is required. This thesis focuses on reinforcing this dike with the new technique of dike pins. Dike pins are grouted steel anchors, that are installed in the dike crest to improve macro-stability. The case study shows that the governing geometrical parameter in design is the centre-to-centre distance of the dike pins. The cohesion of the clay slope was the governing geotechnical parameter for the determination of the slope safety factor. Arching occurred for high values of the friction angle or the cohesion of the sand layer. A large decrease in the bending moment of the dike pin results from arching. In this parametric study, correspondence was found between the 2D and 3D Plaxis models in terms of slope safety factor and in terms of the development of internal moments in the dike pin. A design scheme was suggested, which shows that in most cases a 2D design method may be chosen. The proposed design scheme simplifies the design method for dike pins.

One of the failure mechanisms for water retaining structures is piping. Piping is an internal erosion mechanism creating hollow spaces (pipes) underneath, for example, a dike as a result of the transport of soil particles due to seepage. The formation of pipes can cause collapse of the structure once the erosion process reaches the outside of the dike. This study focusses specifically on the possibility of the occurrence of this failure mechanism in the Maasvallei area. The Maasvallei covers the area of the Maas roughly between the Dutch towns Roermond and Mook. The early signs of piping in the form of sand boils are frequently observed during periods of high water levels in the Dutch rivers. Although the total collapse of a dike in the Netherlands due to piping has not occurred in the past decades, the frequent observation of the early signs of the piping process has resulted in the inclusion of the piping failure mechanism in the Dutch legal safety assessment regulations for water retaining structures. During recent high-water periods in 2011 and 2012 sand boils were observed along several Dutch rivers except at the dikes along the Maas. The striking absence of sand boils in the Maasvallei area raised the question if the failure mechanism piping is relevant for this specific area. In the recent assessment of the Dutch dikes, many of the dikes along the Maas in Limburg were found to be insufficiently safe against piping. The dilemma then becomes clear: the lack of early signs of piping contradicts the outcome of the safety assessment. Resources could be saved if the dikes do not need to be reinforced for piping, however, the safety should not be compromised. Within the thesis this dilemma is studied. The main question that is answered is: Is dike-failure due to piping realistic in the Maasvallei?

Seismic design codes are currently moving from a force-based design approach to a performance-based design approach. For example, in a performance-based design approach it could be specified how many lanes must be available during the lifetime of a bridge given a certain earthquake intensity.The problem with this approach is that it is not specified what the probability must be that the performance criterion is satisfied. This raises the question whether the design codes are acceptably safe or not. Focus is laid on the Canadian Highway Bridge Design Code (CHBDC), in which a total resistance factor approach is used. Because the total resistance factor in the CHBDC is a multiplicative factor, lower resistance factors lead to stronger foundation designs. The goal of this thesis is to calibrate the design procedure in the CHBDC for geotechnical systems under seismic loading, by finding a relationship between resistance factors and the lifetime probabilities of failure of said systems. The resistance factor can then be fine-tuned to a lifetime probability of failure that is consistent with the lifetime probability of failure targeted in static design. As an example problem, the bearing capacity of a shallow foundation on a clay with a pseudo-dynamic earthquake load is tested. The research question that is answered in this thesis is: "What should the resistance factors for geotechnical seismic design be in order to achieve a target lifetime probability of failure that is consistent with static design targets?'' Not every possible combination of soil strengths and forces on the superstructure can be taken into account, and therefore the random finite element method is used in a Monte Carlo simulation. Thousands of realization sare performed for each resistance factor, design return period, and "actual''return period that the designed foundations are tested against. By seeing how many realizations of the Monte Carlo simulation fail given a certain earthquake intensity, the conditional probability of failure given that earthquake intensity can be estimated. The total lifetime probability of failure can then be estimated from the conditional probabilities of failure with the total probability theorem. As part of a parametric study, the lifetime probabilities of failure are estimated for six different scenarios, each of which has different sources of uncertainty.  The resulting lifetime probabilities of failure are interpolated in order to find a resistance factor that targets a lifetime probability of failure consistent with static design targets. Currently, the resistance factor that the CHBDC recommends for geotechnical systems under seismic loading are defined as the static resistance factor for that geotechnical system incremented with 0.20, meaning that compared to static design, weaker foundations are designed for seismic load cases. The resistance factor found in this thesis is closer to the resistance factor for static design than to the resistance factor for seismic design. It should therefore be considered to lower the seismic resistance factor to the value of the static resistance factor so that a sufficient lifetime reliability can be targeted.

The subsurface is often modelled as multiple homogeneous soil layers. In reality, the soil properties of these layers are heterogeneous and spatially variable, making it difficult to properly deduct the engineering properties that are required in the design of geotechnical structures. This leads to uncertainty in the design. The probabilistic framework known as the random finite element method (RFEM) can take the spatial variability of soil properties into account in geotechnical designs in an effort to reduce the uncertainty. The spatial variability is represented by the mean, the standard deviation and the scale of fluctuation. The scale of fluctuation is defined as the distance in which a significant correlation is found within the soil properties and is related to the geological deposition of the soil layer. The calculated reliability of man-made structures, such as dykes, is the output of the RFEM and is influenced by the scales of fluctuation of the subsurface. Since many man-made structures in the Netherlands are constructed on soft soils, they cause deformations in the subsurface. These deformations change the geological layering of the soil. It is therefore expected that the deformations caused by man-made structures influence the scales of fluctuation and that the changed scales of fluctuation influence the calculated reliability of the man-made structures. The objective of this thesis is to research how the spatial variability of soft soils is influenced by man-made structures. To research this, a case study is undertaken at the Leendert de Boerspolder in the Netherlands. One-hundred cone penetration tests (CPTs) have been taken in an area of 15 by 50 meters in the polder as well as in the dyke as part of the research programme Reliable Dykes. From the cone resistance data of the CPTs the spatial variability of the area can be estimated. The case study is accompanied by two theoretical studies. The first study aims to estimate the effect of deformations on the spatial variability of generated random field data for different types of deformations. The second study of this thesis will provide the deformations that have occurred in the area of the case study from a plane-strain finite element analysis of the dyke and polder. The first part of the research focussed on four deformations that are often encountered in the proximity of a dyke: vertical compression, horizontal compression, simple shear and rotation. The effect of these deformations on the spatial variability has been studied by applying the deformations to three resolutions of random fields and then estimating the change in scales of fluctuation. Since no soil properties were assigned to the random fields, the results can only be used qualitatively. The research is then continued with the estimation of the spatial variability of the Leendert de Boerspolder. It was necessary to identify the soil layers first. These are a top peat layer, a clay layer which shows a transition from organic at the top to silty at the bottom, and a bottom peat layer. For each of the CPT lines parallel to the dyke the outliers of the cone resistance data were removed for the different soil layers and the depth trends were removed. This resulted in normalised cone resistance data from which the spatial variability in different directions could be estimated. Finally, a two-dimensional plane strain analysis of the soil layers at the Leendert de Boerspolder was made. In the first step of the analysis the depths of the soil layers are at the level before construction of the dyke. Then the dyke was constructed step-wise. This allowed the initial soil layers to deform as close as possible to the actual deformations under influence of the dyke. Finally, the following conclusions are made by combining the resulting deformations with the results of the other research. At the Leendert de Boerspolder, the spatial variability of the polder next to the dyke is not influenced by the dyke and can be used as the baseline spatial variability to which to compare the spatial variability in the proximity of the dyke. Underneath the crest a significant vertical compression causes both the vertical and horizontal scales of fluctuation to decrease, while a smaller amount causes a change in just the vertical scale of fluctuation. Underneath the slope and toe of the dyke, rotation increases the larger vertical scale of fluctuation and decreases the larger horizontal scale of fluctuation. Horizontal extension of the soft soil underneath the slope results in a larger horizontal scale of fluctuation. Horizontal compression underneath the toe results in a smaller horizontal scale of fluctuation.

The starting point of this thesis lies in the area on Groningen, Netherlands. More specifically, induced earthquake activity is observed in this area due to gas extraction activities, which reduce underground gas pressure. In combination with the location’s geomorphology, liquefaction can occur due to earthquake excitations. Furthermore, the area of Groningen is a location with urban activity and infrastructure, such as pipelines, present. The post-liquefaction effect of these pipelines is their uplift, which can lead to failure, along with all its negative consequences. Furthermore, the creation of two different models, capable of describing the soil-structure interaction of pipelines and post-liquefied soil was the main objective of this thesis. The means by which these models were created was the implementation of the spring and dashpot method. More specifically, Kelvin-Voigt models were used for the ground’s behaviour to be modelled. These models required two main parameters to be specified in each case, the spring coefficient (k) and the dashpot coefficient (c). In order for the spring coefficient to be determined, the creation and usage of post-liquefaction p-y curves was deemed necessary while the problem specific dashpot coefficients used, had previously been determined by means of physical modelling. The ground profile consisted of fully saturated loose sand and the pipes investigated had diameters of 110, 160 and 200mm. The first model was a single degree of freedom one, with that being the vertical. As for the second one, it was a multi degree of freedom one. More specifically, it consisted on two degrees of freedom, the vertical and horizontal ones. The results of these models were validated by comparison to previous studies and further investigation of affecting parameters was carried out. More specifically, the way and the degree up to which several parameters of both ground and structure characteristics affect their interaction were investigated. More specifically, the first parameters considered were the pipelines’ diameter as well as their weight, resulting from their geometry and transported material. Next, the effect of the pipelines’ burial depth was considered and then, the effect of the soil’s initial stiffness. Finally, the effect of the dashpot coefficient was investigated for the multi degree of freedom models. A comparison between single and multi-degree of freedom solution results was also carried out. The results of this study were validated by comparison to previous research findings. Most results and conclusions were in complete agreement with the so far existing bibliography. However, what was found to be inaccurate was the previously determined dashpot coefficient for 110mm diameter pipelines and hence, these were left out of scope of study.

As the construction of sub-aerial and submarine geotechnical structures increase in amount, rate and size, so do their associated risks. Often, with use constitutive models, finite element analyses (FEAs) are performed in order to identify and mitigate these risks. NorSand, which is a consti- tutive model based on critical state soil mechanics for particulate materials (e.g., sand), is one of the first models to integrate the state parameter ψ into its constitutive framework to model dense and loose sands material with the same parameter set. Importantly, it is able to identify the liquefaction potential as it can simulate softening behaviour due to pore pressure increase of loose soils in undrained conditions. Since NorSand has recently been implement into PLAXIS, a geotechnical analysis software capable of performing FEAs, it must be verified, validated and applied with the software, which is done in this report. First, stress-path and parametric analyses were conducted at single stress points. The stress- path analyses show how the state variables evolve for different triaxial conditions. Systematically changing the input parameters to extremes found in literature helped determine their influence on the evolution of stresses and strains. The resulting figures can be used to help future calibrations to experimental lab test data. The PLAXIS implemented NorSand (PLAXIS NorSand) was verified by comparing it with an implementation written in Visual Basic for Applications (VBA NorSand) by the authors of the model Jefferies and Been. Verification in this context means determining if PLAXIS NorSand is able to produce outputs as intended by the authors. Various testing conditions, both triaxial and direct simple shear, showed overlap and agreement between the outputs of both implementations, verifying PLAXIS NorSand. Then, the model was compared to, albeit not in a traditional sense, an ’analytical solution’, which is the relationship between the mobilized friction ratio Mi and state parameter ψ in its simplest form. The mobilized friction ratio and stress ratio at peak strength of PLAXIS NorSand and the ’analytical solution’ were compared. The values between both showed less than 3% difference, further verifying PLAXIS NorSand. The constitutive model was then validated - i.e., established that PLAXIS NorSand is able to approximate soil behaviour as intended. First, by using the soil parameter set that had been derived from lab tests of Erksak sand as a baseline, the input parameters were varied until PLAXIS NorSand was calibrated to individual triaxial tests as best as possible. Then, triaxial tests of Erksak, Nerlerk and Ticino sand were approximated with PLAXIS NorSand without changing the soil parameters determined from lab test data. PLAXIS NorSand is able to follow lab test data decently well with one parameter set. And if one decides to take the time and calibrate individual lab tests, and deviate from soil parameters determined from a set of lab tests, they can be matched even better. Additionally, it showed a consistent need for activation of the softening flag (S = 1) in order to appropriately model loose soils in undrained conditions. Furthermore, NorSand exhibits indefinite hardening in dense soils during undrained loading, which can be avoided by employing a ’cavitation cut-off’. The last part of this report tested PLAXIS NorSand by applying it in FEAs of a simplified submerged landslide, which was subjected to 20 centimeters of displacement at the crest through a rigid slab in undrained conditions. First, the difference in slope behaviour due to change in soil density within NorSand was determined: dense soil resulted in the slope to be able to bear the full 20 centimeter displacement, whereas increasing the void ratio (i.e., increasing the positive value for the state parameter) gave the effect of even quicker slope collapse and a lower bearing capacity. In other words, when using NorSand, the looser soil the further the failure surface moves up and the quicker the structure fails to maintain equilibrium. Lastly, NorSand was compared to Modified Cam-Clay and Mohr-Coulomb to highlight the differences in their ability to model static liquefaction, while being triggered by unrealistic loading conditions. Even though none of the FEAs showed actual liquefaction, since it is accompanied with the fluidization and loss of structure, they still gave in indication of the liquefaction potential. NorSand, contrary to the other constitutive models, showed the expected high sensitivity to forced displacement resulting in clear shear bands resembling Prandtl-type failure mechanism and early onset soil body collapse.

One of the most severe deteriorations in reinforced concrete structures is associated with reinforcement corrosion, where the corrosion distribution shows considerable spatial variability. In the existing investigations of spatial variability of corrosion on the reliability of reinforced concrete structures, symbolic expressions are used for the structural performance. However, structural behaviors like stress redistribution and plasticity spread are not captured. In this research, a computational framework is designed to couple the probabilistic analysis with the nonlinear finite element analysis. Random fields is used with the computational framework to represent the spatial variability of corrosion.A 60 m girder of a reinforced concrete bridge is taken as the case study to explore the effect of spatial variability of corrosion on reliability of static indeterminate reinforced concrete structures. The reliability analysis is target on ultimate capacity of the beam to carry the traffic load. The girder is modeled as a 3 span continuous beam. The modelling of corrosion damages on reinforcement (area of cross section and physical properties) is based on assumption of pure pitting corrosion. In the axial direction of the beam, spatial variability is modeled with random field. In order to study the effect of different level of spatial variability, the correlation length of the random field is set from infinite large to 125 mm. Between adjacent bars, extreme cases of fully spatial correlated and totally spatial independent are studied.The case study shows:i) when corrosion develops, pitting corrosion can severely reduce resistance of the structure and localized damage may lead to a brittle structural response.ii) spatial variability of pitting corrosion in the axial direction of the beam leads to higher failure probability of the structure.iii) spatial variability of pitting corrosion between adjacent bars leads to lower failure probability of the structure.iv) the effect of spatial variability of corrosion on reliability of static indeterminate reinforced concrete structure is a collective effect of probabilistic and physical characteristic.In order to facilitate the reliability assessment of corroded reinforced concrete structures, additional efforts are also contributed to: quantification of uncertainty for the bond model of corroded reinforcement; comparison of various reliability methods with the probabilistic nonlinear finite element analysis framework.The thesis fills the knowledge gap of probabilistic nonlinear finite element analysis of reinforced concrete structures with spatial varied corrosion and quantifies the effects of spatial variability of corrosion on the reliability of a static indeterminate reinforced concrete structure. The analysis framework designed in this thesis is also applicable for other reliability assessment of corroded reinforced concrete structures.

The Dutch Water board revised their guidelines for the safety assessment of dikes in 2017. A major change for the assessment of macro-stability is the use of the SHANSEP method to estimate the strength of impermeable cohesive layers. The failure probabilities are estimated with a deterministic analysis using limit equilibrium methods. The use of design values and safety factors to account for uncertainty is basic and proven to be conservative leading to over engineering. In this thesis, it is investigated how the SHANSEP method can be incorporated to the more advanced Random Finite Element Method. It is found that three random fields for SHANSEP parameters S,m and POP are required. The random fields do not show particular trends in mean or standard deviation. A random field generator is coded in Python. a simple version of the in-house FEM is modified to read the generated random fields. This code is used to test various geotechnical assumptions. A final version of the assumptions is coded into a more advanced version of the simulator to do the comparison. The output of the FEM code are the FOS and failure mechanism of a single evaluation with a combination of three random fields. A mean and standard deviation of the FOS results are calculated. The probability of failure is estimated by the area under the probability density function of a lognormal distribution for values below unity. The probability of failure of the deterministic case is estimated using the First Order Second Moment method. The results show that the probability of failure is overestimated in a FOSM analysis by one order of magnitude compared to the most conservative RFEM simulation. It is expected that this difference is even higher for the more conservative deterministic approach the Dutch guidelines prescribe. The slip surfaces of RFEM were found to be similar to their deterministic counterpart. The RFEM slip surfaces went through local weak zones in random fields. It is recommended to Dutch policy makers to investigate the use the random finite element method. Although conservatism is preferable in safety assessments, an conservatism of this significance compared to the RFEM approach is unnecessarily costly.

In this report, an experimental investigation of the influence of currents on submarine slope stability is presented for the Eastern Scheldt storm surge barrier case. Slope instabilities, including liquefaction failures, have been observed in the scour hole slopes near this barrier. The currents above the sloping bed are expected to initiate the liquefaction slope failures. The effects of the excess pore water pressure increase, that is generated by the currents, on the soil response are investigated by triaxial tests. Multiple excess pore water pressure rates are applied on a loose soil sample. The triaxial tests show that higher excess pore water pressure rates result in earlier developments of strains at lower stress ratios. This research is intended as a step towards a better understanding of the initiation mechanism of the liquefaction slope failures near the barrier.

Displacement control is of utmost importance in deep excavation design and is usually based on numerical modelling, e.g. Finite Element Method (FEM). Numerical methods tend to be more conservative when analysing soil behaviour during deep excavation, whereas for practical and economic reasons this is not favoured. The inverse analysis allows for the identification of the soil parameter set that can provide the measurements observed in the monitoring when it is applied in the model. When performed in a probabilistic concept, it reduces parameter uncertainty and enables the stochastic prediction of future soil behaviour. In this thesis, capabilities and limitations of difference advanced constitutive models are investigated. The Generalized Hardening Soil Small strain model (GHS) presents a positive aspect in modelling soil behaviour during deep excavation with its various stress/strain dependency settings. Because of the uncertainties originating from the size of the domain and limitations of site investigation, the soil parameters can only be shown as probability distributions. In order to make that distribution more accurate, comparative selection of several inverse analysis optimization algorithms is performed. Thereafter, choice of the relevant parameters is done based on the conducted sensitivity analysis and engineering judgement. Having the most competitive optimization approach selected, remote scripting with Python is used to utilise Finite Element (FE) modelling in the 2D Plaxis software. The input parameters are iteratively updated with response observation (diaphragm wall deflections) using the Ensemble Kalman filter optimisation algorithm based on a chosen excavation stage. The re-calibrated parameters are checked with the data, which was used to create synthetic measurements made using the same FE, to perform reliability assessment of the developed Python-based algorithm and investigate its capabilities and limitations. The further development of the presented optimisation method is expected to increase certainty in setting alarm thresholds in the applications of the Observational Method.

The numerical modelling of a cone penetration test (CPT) has long been a challenging task due to the large deformations associated with the penetration of a CPT. Recent developments in advanced numerical methods have shown promising results in overcoming these difficulties by using the Material Point Method (MPM). In this thesis it is researched whether the MPM is able to reliably produce CPT results in dry sand by using a state-dependent constitutive model. Calibration chamber (CC) tests are modelled for dry sand and results are compared with experimentally performed CC tests in the laboratory. Features regarding the numerical setup and applied boundary conditions which quantitatively influence modelling results are identified and assessed before the model is validated to real CC test data. Validation results show that the model is able to accurately produce cone resistance values for different types of sand for soil states that can be categorised as moderately-dense to dense. Last, it is shown how parameters within the constitutive framework affect the model output and a quantification of the sensitivity of the parameters to model results is presented.

In the northern part of the Netherlands, the exploitation of gas fields has been inducing small earthquakes, causing damage to existing buildings. With the aim of preventing consequences to people and structures, the VIIA Groningen project deals with CC2 and CC3 buildings retrofit and provides reinforcement measures when necessary. As part of the structural response assessment, after the NPR 9998 (2015), and eventual special cases from the latest NPR 9998 (2017), non-linear time history analyses (NLTH) are executed, comprising seismic ground response analysis (SRA). The propagation of seismic waves through a 1D soil column is highly dependent on the characteristics of the materials constituting the soil deposits. Hence, it is essential to correctly interpret the soil properties, in order to achieve realistic representations of the in-situ conditions. To interpret the soil layering at a particular site, the Cone Penetration Test (CPT) is commonly used in Groningen. It offers a quick, economical and reliable measurement of ground conditions. However, the CPT-based correlations used to estimate soil properties can constitute a source of uncertainty if not coupled with full-scale testing and laboratory measurements. The present thesis, thus, deals with the verification and the improvement of two CPT-based correlations used for soil interpretation in Gronigen specifically. The research study focuses on the mathematical models related to the plasticity index (PI) and the undrained shear strength (Su) of soft soils present in Groningen. A comprehensive database of factual data was compiled in order to group various test types and provide a best-estimate of soil properties for different soil types using geotechnical and stratigraphic considerations. Secondly, a statistical characterisation of data-sets was performed to obtain insight on the correlations performance in relation to the in-situ and laboratory measurements. Based on the outcomes of the statistical comparison, analytical and regression analyses were carried out with the scope of improving the correlation that was deemed to be inadequate. Additionally, a sensitivity analysis was executed to investigate the influence of three relevant soil properties on the seismic ground response from a typical soil profile from Groningen. The parameters assessed are: plasticity index (PI), undrained shear strength (Su), and shear wave velocity (Vs). Results indicate that, among the considered CPT-based correlations, the equation for PI from Cetin and Ozan (2009) is adequate in some cases. The geotechnical units sandy Clay and Loam show good correspondence with the factual data. On the other hand, the PI predicted with such relation tends to be lower than the laboratory measurements for the remaining soil units (e.g. clean Clay, silty Clay, OC Clay). Conversely, the PI behind the models implemented in the NPR 9998 (Bommer et al., 2017a) are in closer agreement to the factual data, however, the PI from some soil units can be further improved with the findings from the present research. For the interpretation of Su, the SHANSEP model from Ladd and Foott (1974) is frequently used. The available factual data showed a poor correspondence with the predicted Su values. Therefore, the SHANSEP model was further studied to calibrate its parameters for different soil types. From the available triaxial consolidated undrained laboratory tests, best-estimate of SHANSEP coefficients were obtained for the main soil types (clean, sandy, and silty Clay). New Su values were validated with the in-situ and laboratory measurements. In this context, it is confirmed that the dependency of Su on the overconsolidation ratio (OCR) is crucial. Moreover, the estimation of OCR from CPT measurements (following the Mayne, 2014, procedure) is found to be partially inaccurate within the SHANSEP framework and needs to be studied in more detail. Engineering aspects related to the topics of the research are discussed and considerations regarding the applicability of the new correlations are provided. Furthermore, the present study gives indications about the usefulness of a number of test types, suggesting direction for future soil investigations. In addition, look-uptables for PI and Su, based on the outcomes of the present research, are provided as part of the recommendations for implementation in the soil parameter interpretation for the Groningen region.

The Netherlands is prone to flooding as more than a quarter of the country lies under sea level. To combat flooding and ensure that the country remains dry structures such are levees and dikes have been installed. However, older water retaining structures are more than ever failing the stringent safety standard assessments. These older conventional reinforcement measures, including berm constructions, are not only costly but require an expanse of ground to ensure performability. Backward erosion piping is an internal erosion mechanism during which shallow pipes are formed in the direction opposite to the flow underneath water-retain structures as a result of the gradual removal of low cohesive material by the action of water. This mechanism is an important failure mechanism in both levees and dams where a cohesive layer covers a sand layer. Although failure resulting from backward erosion piping is not common, several levee failures in the United States, China and the Netherlands have been attributed to this mechanism. There are mitigation measures known to stop the backward erosion mechanism. One such measure is the placement of a seepage wall, to create a physical barrier directly in the flow path trying to reach the lowest region of the hydraulic head. A review of the literature showed that current design rules only consider groundwater flow calculations when determining the likelihood of hydraulic heave, one of the failure modes within the backward erosion process. Hydraulic heave in the backward erosion piping context is closely linked to the quicksand condition, essentially stating that once the effective stress is zero, the sand particles become suspended, liquifying a solid layer. The absence of an assessment of the effective stresses during the design process in conjunction with hydraulic heave has contributed to the main research question addressed by this thesis; How does a restricted exit for groundwater flow affect hydraulic heave compared to Terzaghi’s free exit situation?.

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

This thesis presents an investigation of the use and applicability of statistical methods in site investigation and subsequent analyses of dykes and embankments. This comprises a comprehensive site investigation via Cone Penetration Tests (CPTs) and laboratory experiments on sampled material, a large scale field test, and statistical analysis of both the site investigation data and the failure test. This work offers the potential to better design site investigations in order to provide reliable estimates of heterogeneity and to demonstrate how these can be used in practical analyses. Such analyses are computationally expensive, but can offer significant benefits in reducing the requirements of dyke upgrades.@en

Highway embankments, river dykes and sea dykes usually have a uniform cross-section and extend for a long distance in the third dimension. These long soil structures are generally characterised by spatially varying soil properties, i.e. soil heterogeneity. Slope stability failures of these structures may have significant economic and societal consequences. Thus, it is of particular interest for engineers to investigate the influence of soil spatial variability on the stability and failure mechanisms of long ‘linear’ structures. For example, earthen levee flood protection systems can be viewed as series systems, where failure at one location, or failure of one component, can result in catastrophic failure of the entire flood protection system and result in tragic loss of life, damage to fundamental infrastructure, and substantial economic impact to the immediate and surrounding regions. In order to ensure the desired level of flood protection system performance, standards in the Netherlands explicitly require probabilistic designs. For example, this may include the use of semi-analytical tools, such as Calle’s 2.5D method and the 3D method of Vanmarcke. However, these (semi-) analytical models make certain simplifying assumptions; in particular, that of a finite length cylindrical failure mechanism. The random finite element method (RFEM) has found increasing use for long engineered slopes in recent years, due to its conceptual simplicity to implement and its capability to comprehensively analyse the effects of soil spatial variability. As a simulation method, RFEM can be applied to large and complex systems, without the need to include some of the rigid idealisations and/or simplifications necessary for analytical solutions, resulting in more realistic models. Therefore, RFEMcan be used as a comparative tool in investigating the performance of simpler methods. Its biggest disadvantage is that it tends to be computationally expensive. The main body of this thesis is devoted to comparative studies (in terms of statistics of the realised factor of safety, the reliability and the failure consequences with respect to potential failure length and volume) of the three above models, for a range of spatial statistics of the soil shear strength. In particular, the relative performance of RFEM and Vanmarcke’s model is investigated for a relatively short slope (of length 10 times the height) for which the length effect may be ignored. For horizontal scales of fluctuation that are large compared to the slope length, the two approaches give similar results, because most of the failure surfaces computed in the RFEM analyses are then approximately cylindrical and propagate along the entire length of the slope, thereby matching Vanmarcke’s assumption and resulting failure length for this limiting condition. In contrast, for smaller values (i.e. less than the slope length), the two approaches can give significantly different results, with the RFEM response of the slope generally being much weaker than the Vanmarcke solution, apparently due to different predicted failure lengths and the influence of the cylinder ends in the simpler model. A second comparative study using all three models involves the so-called length effect (i.e. the increase of the probability of failure as the total slope length increases) for very long slopes (of length up to 100 times the height), using HPC strategies developed in this thesis. In contrast to the level crossing approach adopted in the two (semi-) analytical models, a simple power law equation was utilised with RFEM, which was validated based on the principles of probability of multiple independent (failure) events within the length of the slope. It is shown that RFEM predicts the smallest reliability indices for the range of cases considered. However, the solutions predicted by Vanmarcke’s and Calle’s models move closer to the RFEMresults at larger horizontal scales of fluctuation. Discrete failure lengths have been quantified in RFEMand comparedwith predicted failure lengths using the simpler models, in order to provide a rational explanation for the differences observed. Moreover, the ® factor used with Calle’s model in Dutch practice was investigated thoroughly via random fields for various degrees of spatial variability, enabling a comprehensive evaluation of its influence. While the unconditional RFEM is used as a baseline stochastic method to make the comparative studies, the conditional RFEM was implemented and applied in the last part of the thesis to two example geotechnical applications. The first example focuses on the efficient design of site investigation plans (i.e. optimum locations and sampling intensity) in a 3D soil deposit. A sampling efficiency index was defined and used as an indicator of the efficiency of a site’s plan. A ‘posterior’ distribution of the structure performance, after taking account of the spatial distribution of all the measured CPT data, was derived and showed a significant reduction in the uncertainty compared to the ‘prior’ distribution of the structure response by using the unconditional simulation based on random field theory. An optimal sampling position for the excavation of a slope was identified, both for a single stage of site investigation and a two stage site investigation. Moreover, an optimal sampling distance of half the horizontal scale of fluctuation was identified when an exponential correlation function is used. The second example is devoted to cost-effective designs of an excavated 3D slope. For the problem analysed, a steeper slope was found to be sufficiently reliable (i.e. in line with Eurocode 7) when conditional random fields were used. This was in contrast to the finding of unconditional simulations, due to the greater uncertainty due to only making partial use of available measurement data. The potential benefit of a 3D conditional simulation in geotechnical cost-effective designs has therefore been highlighted. @en