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 current macrostability safety assessment for primary river dike trajectories in the Netherlands is applied to approach the failure probability of a dike during high water events. However, in the current schematization process that is described in the Wettelijk Beoordelings Instrumentarium (WBI) to assess the macrostability, aleatory and epistemic uncertainties are approached ’sufficiently safe’ by applying design values based on expert judgement via a semi-probabilistic assessment. Several primary river dike sections in the Alblasserwaard do not suffice the current safety standard set for the failure mechanism macrostability. The region is composed of a highly complex subsurface with large spatial variation, resulting in large schematization uncertainties for the macrostability assessment of the primary dike trajectories of the Alblasserwaard. With the recent development of full-probabilistic analysis possibilities in software such as D-Stability, it becomes possible to consider uncertainties as a stochastic variable in the macrostability safety assessment. Including schematization uncertainties within the macrostability safety assessment will improve the approximation of the failure probability of the primary dike trajectory. The largest schematization uncertainties in the macrostability safety assessment are currently considered to be the schematization of the subsurface in a vertical soil profile and the uncertainties in the schematization process of the pore water pressures in the dike during high water events. These uncertainties will be included in the calculation process to investigate the influence on the expected reliability of the primary dikes in the Alblasserwaard region. The subsurface schematization uncertainties are investigated by using soil scenarios to investigate the influence of local subsurface schematization in the vertical soil profile. The simplification of the soil profile and position of the soil layers is considered. The pore water pressures are separated into three components: the hydraulic head in the aquifer, the intrusion length, and the phreatic line. Each component will be included as a stochastic variable in the stability analysis. Fragility curves can be applied to describe the distribution function for each pore water pressure component, where the combined fragility curve will provide the combined failure probability and reliability index that includes the schematization uncertainty of the pore water pressures considered. The soil scenarios can be applied to include schematization uncertainties of the subsurface in the macrostability safety assessment. The analysis showed that the simplification of the subsurface schematization only has a minor influence on the reliability index and failure probability of the case study dike cross-section Kortenhoevendijk. The schematization uncertainties of the pore water pressures can be considered in the macrostability safety assessment by combining the fragility curves of each component describing the pore water pressures underneath the dike. Results of the pore water pressure analysis are that failure probability is improved significantly for case study Kortenhoevendijk by a factor 1000 and case study Bergstoep by a factor 10. The approach to consider schematization uncertainties in the macrostability safety assessment via a full-probabilistic analysis can be used for dike sections prone to the uplift mechanism. This approach provides insight into the influence of schematization uncertainties on the failure probability of a dike cross-section. Including the pore water pressure schematization uncertainties in the macrostability safety assessment can have a significant impact on the outcome of the assessment. Including these uncertainties can make the difference between deciding whether a dike trajectory needs reinforcement, or deciding that reinforcement is not necessary.

The Netherlands is a country that is being threatened by water, both from the rivers and from the sea. The Dutch have built dikes to keep their lands from inundation. To ensure the strength and stability of these dikes, they are being assessed on the basis of several failure mechanisms. One of these failure mechanisms is Backward Erosion Piping, or piping for short. In piping, the current underneath a dike is strong enough to take soil particles with it. Tests on piping in tidal subsoil were conducted in the summer of 2021, where a pipe was found to have grown at greater depth than expected The occurrence of this deeper piping has rarely been seen before, let alone described. This lack of knowledge poses a potential safety risk, as it may underestimate the vulnerability of certain subsoil configurations. Therefore, the objective of this thesis is to develop a comprehensive understanding of deeper piping and identify the key parameters influencing its formation. To achieve this objective, a definition of deeper piping and its differentiation from conventional piping is established. Sub-mechanisms governing deeper piping are examined by analysing the forces responsible for grain movement and the forces that maintain grain stability. A Finite Element Model of the subsoil is constructed to quantify the driving forces within the subsoil, which, when combined with resisting forces, enables the determination of whether deeper piping can occur in a given subsoil configuration. To investigate the factors contributing to deeper piping, a series of simulations are conducted using this Finite Element Model. By varying the parameter values while keeping other factors constant, the influence of each parameter on the occurrence of deeper piping was examined. The analysis revealed that several key parameters significantly affect deeper piping formation, including cohesion force (𝑐), cohesion anisotropy (𝛼𝑐 ), permeability and thickness of the top layer (𝑘0 and 𝐷0, respectively), permeability of underlying layer (𝑘1), permeability anisotropy (𝛼𝑘 ) and representative grain diameter 𝑑𝑟𝑒𝑝. Also, it was found that the entrance configuration plays a large role in deeper pipe formation. These findings provide valuable insights into the mechanisms underlying deeper piping and enhance our ability to identify subsoil configurations that are prone to this phenomenon. These findings enhance the identification of subsoil configurations prone to deeper piping, thereby improving risk assessment and mitigation strategies associated with this failure mechanism.

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.

Since 2017, Dutch flood defences are assessed according to new safety standards. These standards are based on flooding probabilities and rely on several assumptions and approximations. There are concerns that the combination of these assumptions leads to conservative results. Recently computed probabilities of failure are often much higher than expected by dike managers and the outcomes of former assessment methods. This conservative bias results in a large and expensive reinforcement task in the coming years which can be reduced by improving the current assessment procedure.  One of the reasons for the current conservatism is the assumption of mutual independence of dike sections and failure mechanisms. Currently, the different elements are assessed independently, while failure mechanisms and failure at different dike sections are likely to occur during the same extreme load event. Furthermore, correlations in space and between different parameters are present within the subsoil characteristics. Neglecting these correlations results in rather high estimations of the failure probabilities.  The aim of this thesis is to investigate how correlations affect the reliability assessment of a dike trajectory. To achieve this, an integral, full probabilistic model is developed that enables simultaneous assessment of dike sections and failure mechanisms while accounting for uncertainties and (spatial) correlations within the model input. The model is based on Monte Carlo simulation. The failure probability of a dike trajectory is computed by counting failure if one or more limit state function 푍푗,푘 for failure mechanism 푗 of dike section 푘 returns a negative realisation. Correlations between the model input parameters are provided by means of a Gaussian copula. A particular aspect of the model is the implementation of metamodeling for the assessment of macrostability. This failure mechanism cannot be described by an analytical limit state function that is easily implemented in the Monte Carlo framework. Therefore, metamodels are created by means of Gaussian process regression. This method makes it possible to assess macrostability within an integral, full-probabilistic framework that is able to include interdependencies between e.g. macrostability and piping, within acceptable computation costs. The model is applied to a case study of dike trajectory 43-4, which is located along the Waal between Sprok and Sterreschans, in the east of the Netherlands.  The effects of different plausible correlations have been studied. This research shows that including certain correlations can significantly reduce the assessed failure probabilities, by a factor ten or more in some situations. However, the impact of correlation strongly depends on the situation. The most significant reduction can be achieved for cases in which (1) parameters that play a dominant role in failure of the corresponding mechanism are correlated; (2) the failure probabilities of the different elements are similar, i.e. for a flood defence where failure is not dominated by one dike section or one failure mechanism; and (3) the failure probabilities of the corresponding elements are smaller than approximately 10−3. The model forms a solid, flexible basis that can easily be adapted or extended to improve the understanding about interactions between failure mechanisms, even though some aspects are simplified or neglected. All in all, the conservatism in current safety assessments can be partly solved by considering the interdependencies between mechanisms and dike sections and by approaching a dike trajectory as an integral system.

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.

River dikes in the eastern part of the Netherlands are characterized by a relatively low daily water table. In the unsaturated zone above the water table, a negative pore pressure (matric suction) is present that binds the soil particles together. Suction can be especially large in soils with small grains, such as clay, and increases the strength of a soil due to higher effective stress. High suction in soils has been proven to significantly increase the stability of dikes. However, due to water level variations and other climatic influences such as precipitation and evapotranspiration, suction in a dike will vary over the year and throughout the cross section. The research described in this report aims at evaluating whether there are parts of a cross-section of a dike where soil suction remains throughout a high water event in a river such that an increase in the strength of the soil can be used in stability analyses. The analysis is centered around a case study of an existing dike in the east of the Netherlands and uses time-dependent unsaturated groundwater flow models to simulate the spatially and temporally varying suction for a number of different initial conditions and climatic influences defined by scenarios. The results show that it is very unlikely that suction in the dike will be lost during the summer months. Due to high evapotranspiration, the water content in the dike is low, which results in a lower water table during a high water event and less infiltration in the dike occurs during precipitation. During winter, the probability that suction is lost throughout the dike cross-section is larger and will occur after heavy precipitation with a long duration where the return period is 1 – 10 years. Although in most scenarios some suction will remain present, the amount of suction during the winter is generally low, between 0.5 and 1 meter, which results in an apparent cohesion of 2 – 4 kPa. A simple stability calculation illustrates that the increase in strength in the dike due to suction does not result in a significant increase in the stability of the dike during high water conditions.

In the past few decades, the use of Bayes' theorem in geotechnical engineering has increased significantly. A good amount of work is done on implementing this theorem for improving the knowledge on soil properties, identification of soil strata, and quantifying different uncertainties involved in predicting soil properties. However, the results of using this approach on a geotechnical structure have not been mentioned in the past literature. Hence, in the current work, Bayes' approach is used to predict the soil property parameters and further these parameters are used in slope stability analysis of a basic slope. It is aimed to investigate if the uncertainties in such analysis can be quantified. For this, a simple Bayes' model is developed to predict the input parameters of the soil properties. This model is developed using the PyMC3 package in python which is specially developed to solve Bayes' problems. Along with Bayes' statistics, normal/frequentist statistics is also used to derive the soil properties from two different data sets (3000 data points and 24 data points). To conduct the reliability studies of a slope, a Finite element model developed at TU Delft is used. The results of slope stability analysis obtained using both approaches are further compared. Results clearly show that when uncertainty is involved Bayes' approach encapsulates its effect on calculated FOS whereas the frequentist approach doesn't. This difference in both approaches is observed due to consideration of all the possible values of input parameters by Bayes' approach. With the frequentist approach, a single input parameter is predicted neglecting all the other possible inputs. Hence, it is concluded that using the Bayes' approach better and more reliable results over the frequentist approach by providing more insight about the uncertainties involved in the analysis.

The Water Authority Rivierenland is responsible for periodically assessing the safety of the dike trajectories in the Alblasserwaard region. In 2012, the safety assessment for inner slope macro-stability was performed based on stress dependent design values for the shear strength, based on the cell test collection of the Water Authority. The most recent assessment on the inner slope macro-stability of the Lekdijk has shown a significant deviation from the previous assessment. According to these results, large scale reinforcement works are requested. Before starting any additional soil investigation, the water authority is interested in investigating the sensitivity of the schematization of the shear strength. The transition from the cell test collection to the triaxial and direct simple shear test collection, and therefore the transition from using the Mohr-Coulomb calculation model to the SHANSEP formulation, is expected to have the most impact on the outcome of the macro-stability safety assessment. The influence of the two test collections on the macro-stability safety assessment is analyzed by using a D-Geo-Stability model from the previous safety assessment for one cross-section of the Lekdijk, and transferring the model to D-Stability. The D-Stability model with the cell test collection parameters and the Mohr-Coulomb shear strength calculation model can be adjusted to the triaxial and direct simple shear test collection with SHANSEP shear strength calculation model. The transition from drained to undrained modelling results in a decrease of the shear strength of the soil around the failure surface. Therefore, the transition from the previous to the new test collection has resulted in a lower safety factor in the macro-stability analysis, having a negative impact on the overall macro-stability safety assessment.

The reliability assessment of hydraulic structures, in primary water defences before 2017, is characterised by exceedance probabilities and implicit uncertainty. In January of 2017, the new water law enforces a change in the assessment of primary water defences. The water law requests a probability of flooding when assessing the safety requirements. The studies of VNK1 and 2 are based on this new safety approach and provide background information and a basis for the new water law. A failure probability and explicit uncertainties provide an increase of reliability in the safety judgement of primary water defences and more specifically hydraulic structures. The aim of a more reliable assessment procedure is to some extent limited by the tools prescribed by the water law. The assessment tool Riskeer does not allow the engineers to have transparency in calculations results, which prevents insight into the model behaviour and contribution to the failure probability. To investigate the mechanics contributing to the overall failure probability for hydraulic structures, analysis of the limit states, failure mechanisms and Riskeer software were performed. The results of the analysis were incorporated into a reference model to validate the suspected mechanics. The input for the reference model was a sensitivity analysis and case study, which cover the assessment tracks of Non-Closure and Strength and Stability for hydraulic structures. The aim of this reference model was not to replace the Riskeer software but describe the mechanics in the correct way. Analysis of the schematisation manual and previous assessment software (Ring toets) provided the incorporated failure mechanisms and the specific model that was used to obtain the limit state. Additionally, a fault tree defined how the different failure mechanisms are related. The knowledge of the fault trees combined with sensitivity analysis provided information about the largest contributors to the overall failure probability, regarding resistance and solicitation variables. The dominant solicitation factor in all failure mechanisms was the water level difference. The resistance factor was dominated by the failure probability of Non-Closure in the gate and the strength of a gate element. In the comparison of the reference model with the Riskeer software, the results were similar but not accurate enough to replace one with another. The reference model was significantly influenced by the approximation in the hydraulic boundary condition, which is formed by assuming a distribution for the water level, wave height and wave period. In the testing of the Riskeer software, the software results showed a difference between two levels of the fault tree. The lower level describes the fault tree including all mechanisms and sub-mechanisms. The top level shows the top probability of the fault tree on which extra simulations of scenarios are executed. The Riskeer software showed the top level as the final result, however, the reference model only describes the lower level. The extra simulations work in a conservative capacity and cannot be assessed by the reference model. The main processes in the fault trees were validated by the reference model, as is shown by their characteristics in the sensitivity analysis. Together with the temporary calculation results, a rough validation of the input parameters was feasible in the lower level. In contrast to the top level, where numerous scenarios were simulated without any transparency to what these values entail. The sensitivity analysis also showed the difference of the two levels over the different variables, which is a (almost constant) significant difference.

This report provides a flood risk assessment of the Isiolo River Basin, in collaboration with Nelen & Schuurmans (3Di, FIS Tool) and Zephyr Consulting (SLAMDAM). This flood risk assessment includes a study of the current flood risk management in Kenya, and in the Isiolo River Basin in particular, because the need for proper flood management is urgent: various climate studies predict an increase in rainfall and an increase in flood risk as a result of the effects of climate change. Current flood risk management is inadequate. Kenya has defined 21 flood-prone areas whereof one of them is Isiolo Town. Isiolo Town is located in the ENN basin which is, relatively, the most prone to the effects of climate change compared to the other basins. Furthermore, the ENN basin currently has the highest poverty rate and avoidance of further enlargement in poverty rate is important, so there is a need to mitigate flood risks. Since Isiolo Town is located in the Isiolo River Basin, this basin has been chosen for an in-depth study. The Isiolo River Basin is an Arid Semi-Arid Land region which is often prone to flash floods. Isiolo Town is a flat area located downstream of mountainous area, the rain which falls upstream flows fast downstream and converges into town, often resulting in inundation. Many hazards, both natural and others, are increasing the flood risk in the basin and specifically Isiolo Town. This flood risk demands flood risk mitigation measures. One possible measure is the SLAMDAM. The SLAMDAM is a movable water-filled flood-barrier. One dam has a length of 5 meters and a height of 1 meter and the dams can be connected to a desired length. The water stored in the dam can be used afterwards for irrigation or other uses. To recommend effective areas to implement the SLAMDAM, 3Di and the FIS Tool are used. 3Di is a hydrodynamic model and it creates flood maps for different rain events. These flood maps are used as input for the FIS Tool. The FIS Tool calculates the benefits for deploying the SLAMDAM at a certain location for a particular length. The locations which result in the highest benefit are recommended to deploy the SLAMDAM in case of particular rain events. However, a site visit is required to see whether the modelled situation aligns with the real-life situation and to see whether boundary conditions are met. The SLAMDAM is also compared to other flood risk mitigation measures. Some were analysed using the FIS Tool, whereas others are evaluated based on five self-formulated ranking criteria. These criteria form the base of a scoring matrix where each relevant mitigation measure is scored on. The performed research has shown the SLAMDAM to rank the best compared to other mitigation measures, both when using the scoring matrix and when using the FIS Tool. However, it is highly recommended to use the SLAMDAM in combination with a Flood Early Warning System. In this way the community downstream can be warned in time to deploy the SLAMDAM. The FIS Tool is found to be especially valuable in finding proper locations for deployment and the dam can be stored close to these locations, enabling fast deployment of the dam in case of need.

The application of reliability analysis in geotechnical engineering is relatively new compared to the other sections of civil engineering such as structural engineering and hydraulic engineering. However, due to its increases use in recent years, reliability analysis is planned to be included extensively in the upcoming Eurocode 7 (EN 1997). This research aims to compare the accuracy and efficiency between the applications of 22 selected reliability methods in 9 selected geotechnical engineering problems with various number of independent variables and modes of failure. The accuracy of the reliability methods are determined based on the Probability of Failure (Pf) errors, while the efficiency is based on the number of realizations (N) each method needs. The Monte Carlo Simulation is found to be the most accurate method despite its shortcomings in efficiency (ranked as the least efficient). Moreover, the FOSM method is found to be the most efficient despite its serious shortcoming in accuracy where it is also ranked as the most inaccurate. However, putting both accuracy and efficiency into account, the AK-MCS 0 order is proven to be the best method when applied to the discussed geotechnical engineering problems. The research also points out the necessity to perform multiple reliability methods for each geotechnical engineering problem.

Discontinuities have an important influence on the bulk behaviour of geomaterials. Discontinuities can be physical openings like fractures and joints, interfaces between different material types, or zones with different material behaviour like mortar or reinforcement material. Bulk material behaviour is often determined by the behaviour of the discontinuities by providing preferential pathways for flow or by acting as failure planes. FEM simulations with continuum elements are typically not suitable for modelling discontinuities with no width, due to the inability to model discontinuous fields. One solution is to represent discontinuities using zero-thickness interface elements. Inserting zero-thickness interface elements allows for discretely modelling discontinuous behaviour between neighbouring continuum elements. The continuum elements are then used to represent the bulk behaviour and the zero-thickness interface elements discretely model the discontinuity. A new constitutive law for zero-thickness interface elements that expands the cohesive zone model with friction is formulated in this thesis. The tangential stress response of the interface elements consists of a cohesive and frictional contribution. The cohesive component of the constitutive law is based on the Crisfield’s cohesive elasto-damage model, which is characterised by a linear elastic response to increased relative displacement, followed by degradation of the cohesive strength and stiffness. The elasto-plastic frictional component is based on the Dahl friction model and implemented in parallel to the cohesive component. The implemented new constitutive law is verified in a large variety of loading conditions, including tangential loading, tangential loading with a reversion of loading direction and combinations of mixed-mode loading. The constitutive laws are validated based on shear box experiments performed on London clay where interface elements are used to model a predefined shearing plane. The cohesive and frictional constitutive law can represent confinement-dependent tangential stress and residual stress at large relative displacements. These features, observed in the shear box experiments, could not be reproduced by the purely cohesive constitutive law. This new constitutive law can be used to better model discontinuities in geomaterials represented by zero-thickness interface elements.

In most current dike assessments only the stationary water levels are investigated in the assessment of the stability of the inner slope, while there are differences for all kind of dikes between the stationary and transient pore water pressures and therefore in the stability. This results in a conservative probability of failure, while determination of a probability of failure should not be conservative but should be as realistic as possible. When time dependency is included in a calculation, an average flood duration is used, while the flood duration is highly variable. The following research question is defined to address the problem: “What is the influence of the flood duration on slope stability and in what degree affects the flood duration the design?” The degree of influence of time dependency on the pore water pressures and slope stability depends on dike characteristics, flood wave characteristics and the delay in failure. The basis for answering the research question is the software SEEP/W to model the time dependent pore water pressures and the software SLOPE/W to calculate the safety factor for the stability of the inner slope. In the research theoretical dike are used and there is focused on the flood waves in the Rhine and Meuse. A correlation analysis is performed to get insight in the contribution of different flood wave shape variables to the safety factor. And a probabilistic analysis is performed using transient and stationary water levels to know the differences in probability of failure between taking the shape of a flood wave into account or not. In both probabilistic analyses is varied in the permeability and the strength of the material; the shape of the flood waves is varied in the transient analysis. In this way the contribution of the flood to the probability of failure can be quantified. Dike characteristics The differences in pore water pressure are especially large for dikes that consist of an impermeable material such as clay. When only the subsoil consists of clay, larger differences are expected than when only the dike body consist of clay. However, large differences in pore water pressures do not necessary lead to large differences in the safety factor. The largest differences in safety factor are obtained when uplifting of the hinterland takes place during the stationary state and/ or during the passage of a flood wave. A transient calculation is therefore most useful for dikes with an aquifer and a thin (thinner than 5 m) weak (low POP values) hinterland. Flood wave characteristics The differences in safety factor during a permanent water level and the passage of a flood wave are large when no stationary conditions are reached during the passage of a flood wave. This is the case for high and short flood waves. Both in the Rhine and Meuse, the amount of short waves (< 7days) is high, which increases the influence of a time dependent calculation. Also, the importance of a time dependent calculation increases when the response to the increased pore water pressures is delayed caused by the permeability of the material. The influence of the height of a flood wave on the stability increases when the soil is permeable. Delay in failure Time dependency causes failure of the embankment to not occur simultaneously with the maximum wave height. The flood wave is decisive for the dike failure, but the permeability and the strength of the dike determines the moment of failure. Influence on design Taking time dependency into account leads to higher safety factors and lower probabilities of failure with exception for dikes that consist completely out of sand. For these types of dikes, the probability of failure and safety factors are the same order of magnitude. This could affect the design, because the dikes are safer when time dependency is considered. The strength of the material is the largest contributor to the distribution of safety factors and therefore to the probability of failure (60-95%). Whereas the contribution of the permeability to the probability of failure is small (2-12%), the variation in the height and duration of a flood wave contribute for 2-20% to the probability of failure. In a permeable dike this contribution is mainly determined by the height of a flood wave, while in an impermeable dike the duration of a flood wave is of importance. Considering the influence of time in stability probabilities of failure, this research proved that probabilities of failure taking the duration into account differ significantly from stationary calculations. It is therefore useful to take time dependency into account when determining the correct safety factor for impermeable dikes, but it is not useful in determining the correct safety factor for permeable dikes, because a stationary calculation is sufficient. In clay dikes it is useful to take the variation in height and duration into account, while for a sand dike it is sufficient to only consider the variation in height of a flood wave. When the variation of the duration of a flood wave is not considered, it is recommended to use a representative duration of a flood wave; that results in the same total probability of failure as when the variation of the duration is included. At Lobith the duration of the representative flood wave varies from 13 - 16 days. At Borgharen the representative duration varies between the 10 – 11 days for different dike types.

In this master thesis the current Dutch method of combining failure probabilities at different spatial scales is researched. This method is used in the Dutch flood risk analysis of earthen dikes to assess the probability of flooding. Currently, probabilities of flooding for geotechnical failure mechanisms are obtained which are not considered to be realistic. To obtain more realistic results the following steps are researched; the assessment of cross-sections, scaling to dike sections and combining sections to a dike trajectory. The increase of failure probability over increasing length, known as the length-effect, is of importance in the current Dutch method of combining failure probabilities. This research shows the conservatism of the assessment of cross-sectional failure probabilities and offers possibilities to reduce the length-effect within and between dike sections to obtain more realistic results.

Site characterization is indispensable in the design phase of geotechnical engineering projects. As a key factor in site characterization, the characterization of soil undrained shear strength (Su) is always in the spotlight. Various methods, including laboratory and in-situ tests, have been developed to measure Su. Nevertheless, these measurements are usually sparse at a specific site due to limited time and budget. To enhance Su characterization, other relevant geotechnical investigation data (e.g., cone penetration test data), can be transformed into Su through empirical correlations (referred to as transformation models) to provide more information on Su. Considering this process introduces the transformation uncertainty and a developed transformation model may not be fully applicable to a local site, probabilistic transformation models (PTMs) have been developed to characterize soil parameters in a site-specific way and quantify the uncertainty to augment engineers’ judgement. However, few PTMs incorporate the spatial correlation of soil parameters, especially in the horizontal direction. This limitation hampers the ability to probabilistically characterize Su in 2D/3D space, which is significant in practice. Moreover, estimating the horizontal spatial correlation from pure geotechnical data is challenging because they are typically sparse. In light of these circumstances, this thesis first proposes a PTM-based scheme to probabilistically characterize Su in 2D. Then it is proposed to integrate geophysical data into the scheme. Compared to typical geotechnical investigations, geophysical surveys provide abundant 2D/3D measurement data, which are often correlated with geotechnical data. The fusion of these two data sources benefits characterizing geotechnical data including Su. Particularly the horizontal spatial correlation of Su 2D domain can be estimated from the abundant geophysical data. To be specific, a well-established PTM, MUSIC-X, by which measured Su and other relevant soil parameters can be used to preliminarily characterize Su, is first adopted. In this case, characterization specifically refers to simulating 1D vertical profiles of Su. It is then combined with the intrinsic collocated co-kriging (ICCK) model, by which primary data (i.e., Su) in 2D or theoretically 3D space can be estimated through linearly combining the preliminarily characterized Su from MUSIC-X modelling and observed secondary data (i.e., geophysical data). The secondary parameter considered in this study is interval velocity (Vint). The scheme, to combine the MUSIC-X and ICCK model to estimate Su in 2D space by the fusion of geotechnical and geophysical data, is applied to a real case study at Hollandse Kust (west) wind farm zone to demonstrate its effectiveness. The results indicate that such a scheme can robustly estimate a 2D cross section of Su with quantified uncertainty. A comparative analysis is conducted between the proposed scheme and two alternatives, one lacking preliminary Su characterization (i.e., without MUSIC-X modelling) and one lacking geophysical data, confirming that the proposed scheme has a relatively high accuracy in the estimated cross section. The research reveals it is sensible to combine MUSIC-X and ICCK for 2D Su characterization and brings a new perspective that integrating geotechnical and geophysical data is promising to characterize soil parameters in higher dimensional space.

Levees are earthen structures that are designed to protect land from flooding and are commonly composed of impervious soils and built on sandy foundations. They are sensitive to an erosion process that is known as piping. After several years of investigation into piping, Sellmeijer proposed design rules by curve fitting results of a numerical model. The design rule are currently applied in the assessment of levees, despite being obtained under the assumption of uniform and homogenous subsoils. Consequently, the design rules seem to be fine for standard consultancy, but it is insufficient for heterogeneous and anisotropic. In this thesis, the effects of anisotropy and heterogeneity are analysed in a elementary and a realistic numerical model study in order to improve the design rule of Sellmeijer. In the elementary study, several aquifers compositions are created by adding an artificial element with a different permeability to the body or by varying the permeability of the body depending on direction. The realistic study is a modification of the elementary study since stratified aquifer compositions have been implemented. After each simulation, the critical head computed in the elementary or realistic composition is compared to the critical head computed with Sellmeijer design rules which requires one calculation value of the bulk permeability. To improve the design rules an alternative method to determine the bulk permeability is proposed that assumes that there is curved or radial flow towards the exit point instead of the Dupuit method which assumes that there is only horizontal flow. As a consequence, the bulk permeability is calculated as the geometric or logarithmic mean of the vertical and horizontal permeability. Based on both studies, it can be concluded that both anisotropy and heterogeneity in the aquifer greatly increase the critical head so that heterogeneous and anisotropic aquifers are significantly more resistant to piping. In some cases, the aquifer can withstand a 45% higher water level. Furthermore, Sellmeijer’s design rules more accurately approach the heterogeneous and anisotropic aquifer, if the bulk permeability is determined with the new approach.