The safety of the Dutch dikes depends on various failure mechanisms. Macro stability, a geotechnical failure mechanism, is highly affected by differences in soil strength because the sliding plane propagates through areas of least resistance. The variations in soil properties in space, also known as spatial
variability, are caused by geological processes and determine the locations of weaker zones in a dike. This highlights the importance of incorporating spatial variability into dike stability assessments.

The approach to incorporate spatial variability in the official Dutch assessment framework (WBI2017) relies on various assumptions. It assumes complete local variance reduction and neglects that the failure mechanism propagates through the weaker zones, leading to a mean strength reduction. Moreover, it assumes a default value for the ratio between local and regional variance α = 0.75, which lacks empirical evidence. Another method to incorporate spatial variability in stability calculations is the Random Finite Element Method (RFEM). This probabilistic technique models strong and weak zones through random fields. However, the main drawback is its considerable computation time, making it impractical to use for the assessment of the hundreds of kilometers of dikes in the Netherlands.

To address these issues, this research answers the question: What is an effective approach for incorporating spatial variability in soil into dike stability calculations? The study is divided into two parts: a data analysis and the creation of an RFEM model.

The first part investigated national and regional spatial correlations using variograms. The study found that the local spatial variance cannot be analyzed with variograms based on the national dataset. This is because the variograms average the variance in the local data due to their large scale. Investigating
local variability requires local data with a high enough density and accuracy in the research area.

In the second part, the inclusion of spatial variability was studied for a case study dike using RFEM, which is part of dike trajectory 34-2, located between Willemstad and Noordschans. The research highlighted two differences between assumptions made by RFEM and the WBI2017 method: (1) the
inclusion of statistical uncertainty and (2) the use of different stress components in calculating the undrained shear stress. The results of the different methods can only be compared if these differences are accounted for. Furthermore, the study found that using a probabilistic calculation with α = 0.8 better fits the results of the realistic RFEM model of the case study dike, particularly in the lower tail of the distribution of the results, compared to the default value of α = 0.75. Therefore, it can be concluded that α = 0.8 leads to a more realistic approximation of the probability of failure of this cross-section.

To investigate the importance of this finding, an assessment was carried out following the guidelines of WBI2017 but with α = 0.8. This showed that the probability of failure for dike trajectory 34-2 was reduced by 39.72% but that the safety category of the dike trajectory (for macro stability) remains unchanged.

Therefore, the answer to the research question is that when considering the computational requirements of RFEM, it is more effective to keep using the WBI2017 approach of implementing spatial variability into the input parameters of dike stability calculations with α = 0.75.

These findings are relevant as they validate the use of the current method with the available data. The study used different approaches for incorporating spatial variability in stability calculations and provides valuable insights for future research.

Tailings dam failures are one of the most destructive phenomena in terms of the number of victims and the environmental impact generated. Over the years, different causes have been identified, with flow liquefaction being a prominent factor to consider when assessing the stability of tailings deposits. Due to the complex nature of these events, numerical models are considered an important alternative for the analysis and design phases of tailings dams. These models require the application of appropriate advanced soil constitutive models to reproduce the relevant features of the soil behaviour and, thus, obtain results that are a valid representation of the observations in reality. In this work, the capabilities and limitations of the Clay And Sand Model (CASM), originally proposed by Yu (1995, 1998) and NorSand model (Jefferies, 1993) are assessed using the finite element software PLAXIS in the analysis of flow liquefaction. The criteria considered in the assessment consist of the accuracy of the models to predict the response of the soil under different monotonic loading conditions, the efficiency of the models for their application and the consistency of results obtained from boundary value problems compared with reality.

Both CASM and NorSand are models developed within the critical state soil mechanics framework and use the concept of the state parameter (Been and Jefferies, 1985). However, they present differences in their formulations and assumptions. The performance of the model is explored in this study at three different levels: the material point level, simple boundary value problem level and complex boundary value problem. Different laboratory tests are simulated for the material point level, analysing a single stress point. For the boundary value problems, the construction of an embankment and the well-known Tar Island Dyke flow liquefaction event are simulated. Before applying the models, the implementation of CASM into PLAXIS is widely verified, and additional verification exercises for the NorSand implementation are also presented. Parametric analyses are performed to have a better insight into the effect of the parameters in the response of the models. Moreover, CASM and NorSand calibrated for the same tailings materials are used for the simulations.

Given that most of the model parameters can be estimated through very well established procedures using experimental data, in principle, the calibration of both models is relatively straightforward if the required experimental data is available and when the data is limited, correlations can be used to estimate the parameters of CASM assuming normally consolidated conditions, which is the state at which tailings are often found. The results of the thesis, at the material point level, show that CASM presents limitations to quantitatively predicting the response of dense materials. This is associated with the formulation and assumptions of the model. In the analysis of the boundary value problems, lower strengths and higher stiffness in terms of stress-strain response are obtained with CASM compared with NorSand. Despite these differences, the results of this thesis demonstrate that both CASM and NorSand can successfully reproduce flow liquefaction at the different study levels.

Using an expensive-to-evaluate numerical model, such as a finite element method (FEM) model, is deemed unavoidable in solving modern geotechnical engineering problems. At the same time, the application of reliability analysis in dealing with uncertainties (e.g. soil properties) is increasing rapidly. This could pose a time-wise problem for an FEM model since reliability analysis normally takes much more than only one realization (function call) of the model. It becomes a bigger problem when a design optimization process is taking place. More often than not, design optimization is performed by a ”trial-and-error” method in practice, which the process itself would even take longer just to give engineers the ”sense” of achieving an optimal design (in terms of safety and economy). Therefore, the actual optimality of the design is not systematically proven and quantified. This research proposes a novel reliability-based design optimization (RBDO) method by combining existing theories regarding active-learning Kriging-based Monte Carlo Simulation (AK-MCS) and (1+1)-Covariance Matrix Adaptation evolution scheme ((1+1)-CMA-ES). To achieve accuracy and efficiency, the method consists of four enrichment stages. These enrichment stages ensure the method accurately and efficiently predicts the optimal design combination by considering the reliability constraint. The chosen case study is the reinforcement design of the Starnmeer polder dyke in the Netherlands, which is simulated as an FEM model. Within a limited number of function calls, the proposed RBDO method could accurately predict the optimal dimensions of the dyke that delivers the targeted reliability index. The reliable performance of the proposed method is further demonstrated by solving three analytical optimization problems.

The extraction and processing of mineral and metal ores in the mining industry comes paired with large amounts of mine waste, also known as tailings. This waste consists of various chemicals, acids, and heavy metals which are used during these extraction processes. The tailings are usually stored off in tailings storage facilities (TSF) in a loose state, gradually consolidating over time. TSFs founded in seismically active areas are susceptible to liquefaction due to earthquake loading. Historic data show that about 35% of dam failures are due to liquefaction of the tailings, thus increasing the need to study the liquefaction responses of tailings under cyclic loading. Extensive studies have already been
conducted using cyclic direct simple shear (DSS) and cyclic triaxial (CTX) tests as these tests under constant-volume conditions can evaluate the change in pore pressure within a soil accurately. Previous study shows what importance the relative density and sloping ground conditions, known as drained shear bias, have on the cyclic resistance to liquefaction of the tailings. However, in practice the pore water is not bounded within the material and excess pore water can flow out through installed drains. A round-robin program, issued by the University of Western Australia (UWA), requested a study on the liquefaction response of a particular fine-sand tailings material. Inspired by this round-robin program, an interest raised in studying the cyclic shear response of tailings by using a direct shear box to investigate the cyclic behaviour under partially drained conditions. With use of the direct-shear apparatus of Wille Geotechnik, a test program has
been set up to study the influences of relative density and drained shear bias under stress-controlled cyclic shearing and under constant normal load conditions.
Results of the experiments met the expectations that denser soils have a 9.6% higher cyclic resistance ratio (CRR), and samples with applied drained shear bias have a 32% lower CRR compared to samples tested with level ground conditions. Furthermore, samples which underwent post-cyclic shearing showed strain-hardening responses and yielded higher shear stresses compared to the monotonic test, indicating that the constant normal load further densified the samples during cyclic shearing. However, during the experiments, it was
quickly found out that the loading frequency was not being applied optimally making it not possible to analyse influence of partially drained conditions . This study showed promise on its capabilities to study cyclic shear loading on a soil. For future work, it is suggested to perform similar tests under a uniform loading frequency with the use of a shear box to evaluate its capabilities to study on partially drained conditions. It is also recommended to conduct tests under constant volume conditions, to evaluate the shear-box apparatus’ capabilities to
study the liquefaction response of a soil due to excess pore pressure generation.

Major flooding occurred on the Meuse River in 1993, 1995 and 2021, causing significant damage to regions in NL, BE, DE. The flood events of 1993 and 1995 occurred in the winter, while that of 2021 occurred in the summer. There are large differences in the characteristics of these floods separated by nearly three decades; not only the seasons differ, but the topography of the river bed and the shape of the flood wave have also changed. Since 1995 dikes and flood-routing measures have been constructed along the river. Although all these projects are not yet completed, the flood event of July 2021 indicates that the Meuse projects are producing the expected results. This research aims to understand the effect of the shape of the flood wave during a high-discharge event, the impact of the different types of flood protection along the river and the interaction between the main river and its tributaries. The main research question is: what are the hydrodynamic differences between the high-waters levels on the Meuse in Limburg in 1993, 1995, and 2021, and how can these differences be explained?
The first step to complete this research was to gather the needed information. The second step is to identify the differences between the different flood events and assessing the impact of the different flood protection measures. The third step is to assess the impact of the different flood protection measures.
After an analysis comparing inundation maps, five flood prone areas were identified and investigated, namely: Maastricht, Bunde and Meerssen, Maaseik-Roosteren, Roermond and Venlo. Flood wave characteristics play an important role: the width illustrates the duration of the event, while the height indicates the maximum water level that can be expected.
Theoretical predictions of flood wave behaviour derived by scenario-based simulations with hydraulic models (i.e., report of peak attenuation, evaluation of the Grensmaas and the tool Box of building blocks) were compared with measurement data, water levels, discharges and inundation maps in order to assess if intended effect of certain measures correspond with the measured effect of the flood events of 2021.
The flood event of July 2021, the amount of water already in the river system, before the heavy rainfall in the southern part of the Netherlands, Ahr-Eifel region in Germany, Luxemburg and Eastern part of Belgium, was only approximately 200 m3/s instead of the 600-700 m3/s in 1993 and 1995. This means that there was a large buffer, before the water level increased to dangerous levels. Secondly, the short duration of the flood event in 2021 compared to 1993 and 1995 the increased role of peak attenuation. The flood routing-measures have helped to increase this effectivity due to the fact that more water could be stored in floodplains, high-water channels and retention areas.
For this event it can be concluded that the duration of the flood event in combination with the already executed flood-routing measures have prevented further flooding.

The Port of Rotterdam (PoR) is the largest port in Europe and in order to maintain its status, it would need to expand. For the expansion, an extensive survey of the subsurface is needed for the construction of new port areas and its geotechnical structures. As part of designing the geotechnical structures, the subsurface is often modelled as multiple homogeneous soil layers. However the soil properties are in reality heterogeneous and spatially variable. The spatial variability of a soil property is characterized by a mean, a standard deviation and the scale of fluctuation. The scale of fluctuation is the distance over which a soil property is significantly correlated and it is limited to the soil layer of that soil property. Therefore the change in the geological layering of the soil because of external depositional factors such as river, sea and wind can influence the scales of fluctuations and the resulting geotechnical design.

The objective of this thesis is to look at the spatial variability in the vertical direction of the Pleistocene sand from the Kreftenheye and Boxtel Formation in the Port of Rotterdam and see if the river Meuse has any influence on the spatial variability in the vertical direction. An additional question is asked if the spatial variability has any influence on the computation of the pile base capacity for a single foundation pile and what are the implications of the answer to that question. To answer these questions, four sites in the Maasvlakte, Botlek and Pernis were selected and the cone penetration tests (CPTs) taken at the twelve sites were used for this thesis. An empirical method which uses CPT data to identify soil layers was used to identify the Pleistocene sand layer in the CPT data. The first part of the thesis uses the cone resistance data of the CPTs to estimate the spatial variability of the sites. The second part of the thesis focuses on the additional research question by using random field theory. Per site, the mean, standard deviation and vertical scale of fluctuation θ_v were used to generate simulations of cone resistance data. For each combination of standard deviation and θ_v 500 simulations were carried out. For each simulation the pile base capacity was computed with two CPT-based averaging methods, Koppejan method and LCPC method. The coefficient of variation of pile base capacity is used to measure the uncertainty of the computed pile base capacity.

The results show that the range θ_v values are: 0.26 – 2 m in the Maasvlakte, 0.24 – 1.76 m in the Botlek and 0.14 – 1.18 m in Pernis. In terms of the mean θ_v, you see a gradual increase from the upstream area (Pernis) to the downstream area (Maasvlakte). The increase is from 0.27 – 0.63 m in Pernis to 0.64 – 0.80 m in Botlek to 0.84 – 1.86 m in Maasvlakte. However, it is not clear if this is due to the Meuse or due to the existence of sublayers in the geological formation or due to some other factor. Further investigation is needed before a conclusive answer can be given. The answer for the second part is that as long θ_v is significantly larger than the pile diameter D (θ_v ≥ 4D), it does not influence the uncertainty of the computed pile base capacity. However, the mean and standard deviation of cone resistance does influence the uncertainty of the computed pile base capacities. Finally, it is observed that spatial variability does not play a role in the uncertainty of the computed pile base capacity if the coefficient of variation of the cone resistance c_v (q_c) is small (c_v (q_c) ≤ 0.15). The implication for the uncertainty of the computed pile base capacity and therefore the pile design is that one can afford to have a less accurate description of the spatial variability from using fewer CPTs if θ_v ≥ 4D. The same holds true if c_v(q_c) ≤ 0.15.

Risk-based and probabilistic reliability design methods are starting to be integrated into the daily geotechnical engineering practice, as shown by the current draft of EN1997 (Eurocode 7), which explicitly allows Reliability-based verification of limit states. The semi-probabilistic design methods in EN1997 are a compromise between ease of use and accuracy of the achieved reliability levels. In contrast, EN1990 (Eurocode 0) requires accurate full probabilistic design targets. An assessment to investigate if the semi probabilistic methods from EN1997 comply with the EN1990 reliability targets is therefore necessary since the link between the norms is not explicitly established.
In this study, pile foundations serve as an example to assess compatibility between the EN1990 and EN1997. The deterministic Dutch pile design approach by van Mierlo & Koppejan (1956), CPT based design method, is adapted to the semi probabilistic model pile recipe in the EN1997 draft. This thesis assesses what reliability levels are achieved by the model pile design method in draft EN1997 considering the axial bearing capacity and how these compare to the reliability targets in EN1990.
Methodology: To assess the performance of the model pile method from EN1997, the design outcome from the semi-probabilistic model pile method is compared to fully probabilistic quantification methods of the resistances and loads. Two probabilistic quantifications are used in the assessment, a Bayesian and a Student-T model. The achieved reliabilities are assessed with both the First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). Additional insight into the influence of different parameters is provided with sensitivity analysis and the calibration of partial factors. The assessment was applied in two case studies located in the Netherlands.
In both case studies, the EN1997 designs resulted in reliability levels in good agreement with the reliability targets stated in EN 1990. This suggests an agreement between the semi-probabilistic and the full probabilistic models if sufficient CPTs are used. In both case studies, EN1997 designs accounted for more model uncertainty than the probabilistic models suggest, thus partial model factor (γRd) in EN1997 may be conservative. EN1997 covers spatial variability and uncertainty due to limited observations with the correlation factor (ζ, a factor that transforms calculated to representative values, and the partial resistance factor (γRc). The coverage of uncertainty with these two factors seems to be rather low, especially for situations with few CPTs available (less than 10), although the results seem to depend strongly on the degree of spatial variability in the CPT field. In the case of homogeneous soil conditions between observations, EN1997 design methods led to over-conservative designs for low numbers of observations. If the variability between limited observations (less than 10 CPTs) was high, designs are assessed to be less reliable than EN1990 requires.
Overall, the results suggest good agreement of the semi-probabilistic design methods from EN1997 with the reliability targets defined in EN1990, for designs based on sufficient observations. The sensitivity analysis and isolation of the resistance uncertainty showed for the two cases that the uncertainty of the resistance has the dominating influence on the reliability of the piles, suggesting a low impact of complex stochastic load models. The latter finding suggests that probabilistic treatment of the resistance may be sufficient for assessing pile reliability in practice, while design values could be used for the loads.

Sea level rise will increase the risk of flooding in coastal areas. This poses a risk to the coastal protection as well as rivers and lakes close to the coast. Solutions are needed to cope with this threat. The past decade, nature based solutions have gained significant interest. One of these solutions could be sandy foreshores. Due to the use of natural materials, sandy foreshores are a ‘nature-based solution’ opposed to a more traditional approach of dike reinforcement. For sandy foreshores to be a viable alternative to regular dike reinforcements, the order of magnitude of construction and maintenance costs need to be known. For this reason, it is necessary to be able to calculate a failure probability of a dike with sandy foreshore, to predict the required maintenance and to optimize the design based on life-cycle costs.

To improve the calculation method, a step-wise calculation of the failure probability for wave overtopping of a hybrid structure was developed. The calculation included an iterative process. The calculation methods consists out of calculating the failure probability for wave overtopping in Riskeer and a dune erosion calculation in Xbeach. In this research, overtopping was considered as the dominant failuremechanism. For the assessment, the dike was seen as an impermeable hard layer and the foreshore as a beach. Therefore, dune erosion could not erode the main structure and is considered a sub-mechanism of overtopping.

Next, a calculation was performed to predict the longshore transport along the beach in Almere Duin. The occurrence of different wind directions, together with a Delft3D model of the Markermeer, was combined to find the longshore transport. The LST was calculated with transport formula calibrated for coastal areas. The life cycle costs (LCC), including design and maintenance costs, were calculated for different strategies. The calculated alongshore transport together with cost estimates were used to calculate the LCC. Subsequently, the net present value of the maintenance costs was calculated to determine the LCC for each maintenance strategy. At the end the uncertainty and sensitivity of each strategy were analysed.

The time-varying protection level can be optimized by calculating the failure probability due to wave overtopping, with Riskeer and calculating the erosion of the foreshore, with Xbeach. To use this method, Riskeer and Xbeach should have the same design point and if the design point shifts, an extra iteration is necessary. For a 1/10 profile, only a 0.25 m lowering of the foreshore height was found and one extra iterative step was required to carry out the calculation. A maintenance strategy with a 100 year maintenance interval period was found to be optimal in this thesis and a Monte Carlo simulation, which included uncertainties, led to similar results. However, the total LCC were 21% to 34% higher, when uncertainties were included in the calculation. These findings suggest that it is not necessary, to carry out a probabilistic calculation, to find the optimal maintenance strategy. However, the models used, aswell as the local boundary conditions, such as the longshore transport and the cost of sand, were found to influence the life cycle costs significantly. For this reason, it is concluded that a location specific analysis is important to optimize the maintenance strategy.

Two types of calculations are currently used to assess dikes for macro stability. These are the semi-probabilistic calculation and the probabilistic calculation. In practice, the semi-probabilistic calculation is currently mostly used. However, the probabilistic calculation is the most accurate calculation of the two methods resulting in the most realistic results. Performing a probabilistic calculation is on the other hand less simple and a lot more time consuming. Therefore it would be more efficient to still regularly apply the semi-probabilistic calculation to save time and also find a way to make this calculation more accurate. Although the probabilistic calculation results directly in a reliability index, this is not the case with the semi-probabilistic calculation. To link the target reliability index to the factor of safety of the semi-probabilistic calculation, a calibration formula is used. This formula was made using a set of probabilistic calculations from the calibration study. The formula is designed in such a way that in reality 80% of dike profiles are calculated too conservatively with the semi-probabilistic calculation and 20% not strict enough. This means that this formula results in a lower reliability index for the majority of dike profiles than what the realistic value would be. The result of this conservative formula is that in some cases actual reliability of the dike profile can deviate reasonably from the probabilistic reliability index. Some profiles can therefore be made far too robust, while a few others may be approved unfairly. There could be a lot of profit to be made in both safety and in the amount of reinforcement required if the existing calibration formula can be further elaborated. This leads to the main question of this report: “How can the current calibration equation for the assessment of a dike on macro stability be elaborated by using the results of probabilistic calculations from the calibration study and SAFE?” As emerges in the research question, the probabilistic calculations of two projects are used for the research; the calibration study and the project SAFE. The calibration study is the project from Deltares on which the current calibration formula is based. The set of dikes in this project consists of a mix of local and regional dike profiles around the Netherlands. The set is arranged in such a way that almost every type of dike in the Netherlands appears in it so that it can be applied as widely as possible. In contrast to the dataset from the calibration study, the dataset from SAFE consists of dike profiles of only two dike sections at the Lek. The dike profiles belonging to SAFE have been compiled by the water authority and calculated probabilistically by Sweco and Arcadis. The data set from safe is composed in such a way that the critical dike locations of these 2 sections on the Lek are included. Several ways to see if the current calibration formula can be made more accurate are investigated. Initially, SAFE's location-specific set is compared to the calibration formula. It is checked to which extent SAFE corresponds to this and what the reasons can be for existing differences. It is also examined whether the current calibration formula can be improved on the basis of different dike characteristics. A distinction is made of several general , soil and geometric characteristics. The research shows that SAFE's dike profiles require a slightly different calibration line than the line from the calibration study. Instead of 80%, only 64% of the dike profiles lie below the calibration line of the calibration study from Deltares. Especially at the lower reliability indexes, the profiles from SAFE are not calculated safely enough. It is not demonstrable that the profiles from SAFE lead to different results due to the fairly similar type of dikes from the project or the specific location. The difference will therefore mainly be due to the different calculation methods of both projects. In addition, there were also two dike cases/characteristics that has an influence on the difference in reliability index; the design profiles and the berm. With Both, it seems useful to draw up a special calibration line that takes this into account. Especially a calibration line for only the design profiles produces a much more accurate result. This new calibration line results in 30% more accurate reliability indexes. The conclusion of the report is therefore that it would be effective to apply a separate calibration line for SAFE and for the design profiles. For SAFE, the difference with the current calibration line could also be solved with a better calibrated schematization factor, using frequently probabilistic calculations or by renewing the existing calibration study because the difference that occurs seems to be mainly due to the calculation method. Moreover, a separate calibration line for the design profiles thus produces a lot more accurate results. However, the consequence of these more accurate results is that fewer profiles will be on the positive side of the calibration line. The separate calibration line for the dike profiles without designs is 20% less accurate but resulted in safer calculations. When both formulas for designs and normal profiles are used, the complete data set gets a little more accurate with 8% and also even safer than the current calibration formula. So there is certainly something to be improved from the current calibration formula by distinguishing between dike profiles without design and with design.

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.

The Dutch government provides a calculation method to determine the risks to society outside the boundaries of institutions handling Dangerous Goods (the risk affecting External Safety). The current method to calculate the risk affecting External Safety for train marshalling yards is deterministic, outdated, and not transparent. This thesis aims to improve the calculation method regarding rear-end collisions in automated marshalling. It provides a reliability-based approach to the study case Kijfhoek and uses a multi-body dynamic model to simulate the collisions. A Monte Carlo simulation is performed implementing over twenty-five parameters to determine the probability of damage in case of a rear-end collision. From the results, a simplified method is designed to assess the probability of damage to the wagon’s structure. This method uses a newly found relation to determine the absorbed energy at the impact interface in case of a collision. Furthermore, the simplified method reduced the calculation to five parameters and an analytically solvable Limit State function. A first-order reliability method shows that the impact velocity is the single most important parameter in determining the probability of damage.
The simplified method also allows for site-specific values and gives insight into the system and the most important parameters. It is recommended that this method, to determine damage to especially tank wagons in rear-end collisions, is used to improve the existing calculation method for determining the risk affecting External Safety.

Six cyclic settlement models for sand are evaluated to analyse the settlement of automatic stacking crane (ASC) rail tracks at the Rotterdam World Gateway (RWG) container terminal. During Phase 1 of the RWG container terminal settlement of the rail tracks occurred at multiple locations after the ASCs became operational. This has repeatedly led to (unplanned) downtime of parts of the RWG container terminal due to rail track maintenance. Settlements are caused by densification of the sand fill, which is a result of the cyclic load applied by ASCs moving continuously over their rail tracks.

 

The aim of this research is to contribute to prevent unplanned downtime in Phase 2 of the RWG container terminal due to rail track settlements. Also, reliable settlement predictions can be used to determine the intensity and extent of the ground compaction that are needed to meet the settlement requirement of 20 mm for ASC rail tracks.

 

The cyclic settlement models, which have been validated to predict the cyclic settlement of rail tracks and shallow foundations, are obtained from literature. The available soil data include CPT’s, boreholes and standard laboratory soil testing. In addition, settlements of the ASC rail tracks in Phase 1 had been measured for a period of almost one year. The cyclic settlement models are evaluated at six different locations, where the sand is medium to very dense and settlements up to 32 mm have been measured. The load is modelled as a quasi­static load equivalent to a vertical stress of 60 to 90 kPa applied to the ballast-­sand interface. The model parameters of the cyclic settlement models are determined by correlation, (FE) modelling of the first load cycle, extrapolation and estimation.

 

The zone of influence was found to reach around 6 m below the shallow foundation. Densification of the sand fill is substantial within the entire zone of influence. The maximum densification was found not to coincide with the minimum void ratio, it is a variable that depends on the initial state of the sand and the loading and soil conditions. After order 10⁴ load cycles densification of the sand was found to become negligible. To meet the settlement requirement for ASC rail tracks the sand fill must consist of sand layers with a minimum and average relative density of at least 65% and 85%, respectively.

 

Cyclic settlement increases with the number of load cycles, amplitude of the load and extent of the zone of influence and decreases with relative density, stiffness of the sand and volumetric threshold strain. However, correlations used to calibrate the model parameters lead to model predictions that are over- or insensitive to parameters that affect the cyclic settlement. The cyclic settlement predictions of the terminal density model are most reliable and match best with the settlement measurements, for loose and medium dense sand the model predictions underestimate the settlement.

 

Instead of using correlations to obtain the model parameter values and decrease their uncertainty it is recommended to measure the:

·         disturbance of the sand fill underneath the ASC rail tracks due to construction;

·         maximum densification of the sand underneath ASC rail tracks in Phase 1 at locations where rail track settlement has stopped, i.e. where the sand reached its maximum densification;

·         model parameters that characterise the cyclic densification behaviour of sand in cyclic soil tests.

This will improve the reliability of the cyclic settlement predictions of ASC rail tracks constructed on a sand fill. To validate the cyclic settlement models for ASC rail tracks on sand, measurements of the settlement with depth as function of the number of load cycles are needed.

To reduce the flood risk in areas prone to flooding, possible adaptation measures must be investigated. In this thesis a Python-based framework has been developed that can screen flood adaptation measures as an alternative to the existing analytical method of Royal HaskoningDHV. The framework is limited to the costs and effects on the economic flood risk (the benefits) of eleven different measures such as levees, landfills, and flood proofing. First, the existing methods for screening measures were investigated. The resulting strong and missing elements were combined to form the functional requirements of the framework. The underlying script for the framework was elaborated with these requirements. Subsequently, the framework was applied to two case locations, namely Phu Loc (Vietnam) and Waal Eemhaven (Rotterdam, The Netherlands). Because these locations had already been developed by Royal HaskoningDHV, the results could be compared. The existing methods showed that clear results and the possibility for the user to select the measures and location are the main strengths. In addition, an uncertainty analysis and well-organized input table were found to be useful for the framework. The results of the simulations at the case locations were comparable to the results of the existing method of Royal HaskoningDHV for the measures considered. The framework is faster than the existing method and determines the optimal measure(s) and protection level. Therefore, it is a good alternative for screening the eleven considered measures. The framework can be supported with a hydraulic model to include more measures, for example river widening. It is recommended to add an extensive cost database to the framework, so that cost calculations and uncertainty analysis can be performed more easily in future applications.

Tailings are the rock flour which result from the process of mineral extraction at a mine. This waste material is stored in tailings storage facilities, also known as tailings impoundments. These impound­ments gradually grow in size during operation as more tailings are produced and stored over time. These structures are however also prone to failure. Well known failures in the past years are that of the Feijão and Fundão dams in the Minais Gerais state in Brazil. Static liquefaction of the dams has caused mud­streams in which many people were killed and the environment became heavily polluted. This study researched the probability of rainfall­-induced static liquefaction, as meteorological causes have often been named the trigger of failure. The study was limited to upstream raised decommissioned dams in the Minas Gerais state in Brazil. An analysis methodology was established in which the needed rainfall intensity to failure was calculated for different durations of rainfall. In a geohydrological analysis, the Richards equation for unsaturated flow was solved, to model rainfall infiltration. A quasi­-2D procedure was implemented to allow for a computationally efficient solution. Following the results of the geohydrological analysis, a limit equi­librium method was employed to calculate the factor of safety against liquefaction of the dam. In this case, the undrained strength analysis was applied together with an effective stress analysis to model both liquefiable tailings and non­liquefiable tailings in the tailings storage facility. If the factor of safety was equal to a predefined factor of safety associated with failure, the failure intensity was found. The failure intensity was converted to a return period of failure by the application of the Gumbel distributions that are part of the intensity­-duration­-frequency curve of rainfall. These IDF­-curves describe for all possible combinations of intensity and duration the probability of occurrence. Integration of the IDF­-curve for the failure intensities yields the total return period of failure as a single perfor­mance indicator. The analysis was restricted to a period of 5 days of continuous rainfall (storm events) as evaporation effects were not considered and no longer rainfall events were observed in the precipi­tation data used. A series of sensitivity studies was performed to observe how rainfall influences the stability of a tailings dam. It was found that failure is attributed to a loss of suction in the unsaturated zone upon rainfall in­ filtration as well as a loss of strength due to mounding of the water table. Because of the low strengths that liquefiable tailings have, there was the tendency to develop deep slip surfaces below the phreatic surface, causing only marginally stable dams to be prone to failure because of rainfall infiltration. The factor of safety upon rainfall is reduced in the order of 2 to 5 % depending on the parameters used. The strength parameters were of the largest influence. Increasing the friction angle of the non­-liquefiable tailings by 10 % increases the return period of failure by approximately 400 years. The strength ratios used to model the liquefiable tailings are of even larger influence. Adjusting that by only 2 % leads to a jump in the return period of failure of around 1000 years. The chosen boundary conditions for the phreatic surface in the impoundment were also of great influence. A difference of 0.3 meters for the water table for a dam of 20 meters high brings the dam to marginal stability. Given the little sensitivity to storm events, it is recommended to shift focus towards the behaviour of the phreatic surface over longer simulation periods to model the effect of e.g. extremely wet seasons. In addition, construction defects should be considered in which perched water tables could arise, severely decreasing the stability of a tailings dam.

Soil properties are spatially variable due to the natural deposition process. Because of this inherent spatial variability, a slope can actually fail along any potential slip surface. A single value of Factor of safety cannot account for this variation dominated the slope stability problem. Probabilistic analysis considering the spatial variability is a reasonable method to quantify the risk of the slope stability problem. Thus, in order to better simulate this variation, the theory of random field has been widely used in the slope stability problem. However, statistical outcomes derived from the probabilistic analysis will be influenced by how the random fields are generated and how the random field values are assigned to each potential slip surface. In order to investigate the extent of this influence, this study proposed a new probabilistic slope stability analysis method and compared it with the other two methods in terms of accuracy and efficiency. In this report, three different probabilistic slope stability analysis methods are presented. These methods combined the traditional limit equilibrium method of slices with random fields, which can account for the inherent spatial variability of soil properties. An exponential decaying function is used to describe the correlation structure of this spatial variation. This correlation structure is further expressed by the form of covariance matrix. Since the covariance matrix is a symmetric positive definite matrix, Cholesky decomposition is used to decompose it into the product of two triangular matrices. Because the triangular matrix is more computationally efficient, the two-dimensional random field is generated by multiplying a normal random number vector with the lower triangular matrix derived from Cholesky decomposition.

Climate change is a major problem for today's society, which has a huge impact on water safety issues. Recent IPCC scenarios show that sea level rises of 1m by 2100 and 2m beyond 2200 should be seriously considered. Several scenarios show an increase in river discharge of between 10 and 20 percent of the Rhine generated by extreme precipitation by the year 2050. The combination of the sea level rise and the increase in river discharge has consequences for the flood risk in the Netherlands. The area where most people live, about 3,5 million, and where most of the gross national product, around 65 percent, is earned is the area of dikering 14. This thesis determines how the flood risk changes for future climate change scenarios, considering a sea level rise up to 2m and an associated increase in river discharge. One base case scenario with the current situation and four future scenarios with a sea level rise up to 2m with increments of 0,5m were evaluated. The river dikes along the trajectories of the Hollandse Ijssel, Nieuwe Maas and Nieuwe Waterweg and the dunes between Hoek van Holland and Ijmuiden were assessed and the consequences of flooding due to a dune or dike breach were investigated for all scenarios.

Flood risk is determined by the probability of failure of a flood defence and the consequences in case of a flood, which are expressed in economic damage, casualties and affected persons. The influence of climate change on the probability of flooding of 8 river dike profiles was investigated by assessing the failure mechanism overtopping and overflow, using a relationship between height shortage and the probability of failure. The safety of the dunes was evaluated using the Duros-plus model, with which dune erosion calculations were made. The results show that climate change has a big impact on the probability of failure, which is highest for the trajectory along the Hollandse Ijssel with a probability of failure of 1/370.000 per year in the current situation and 1/170 per year in the scenario involving a 2 m sea level rise. Although the failure probabilities of the dunes are very low in the current situation, the influence of sea level rise is shown for the dunes with failure probabilities that are a factor of 2000-3000 higher in a scenario with 2m sea level rise compared to the base case scenario.

For determining the consequences, both existing flood scenarios for the river side and new flood scenarios for the seaside were used. The new flood scenarios show the effect of sea level rise on the increased flood extent caused by a dune breach for each scenario. The potential economic damage, which is determined by the flood depth, damage curves and the land use map, is highest for a dike failure along the Hollandse Ijssel, as the highest flood depths are reached in these deep polders. The highest number of casualties, 7900, determined by the mortality rates based on flood depth, flow velocity, rise rate and evacuation factor, are expected in case of a dike failure along the Nieuwe Maas, as the densely populated cities of Rotterdam and Schiedam are flooded. By assigning monetary values for casualties and affected persons, the total damage is determined, to which the damages resulting from casualties and affected persons contribute most.

After determining the costs of several reinforcement projects, these costs and the potential total damage were used as input in a cost-benefit analysis, where economic optimums were determined expressed in a probability of failure and associated investment costs. The conclusion is that it is economically efficient to reinforce all flood defences except for the trajectory along the Nieuwe Waterweg in case of a scenario corresponding to 2m sea level rise. It was also examined whether the economic optimums met the requirement that everyone should have a maximum risk of dying due to a flood of 10^-5 per year. A total length of 40,5 km river dikes and 63,5 km of dunes will need to be reinforced, for which the costs of reinforcing the river dikes are significantly higher per km than for the dunes, approximately 20 and 3,8 million euros/km respectively. The total estimated costs determined in this study are around 1 billion euros for a 2m sea level rise scenario, but these costs for keeping the area safe will be a factor of 2-3 higher, as the method used for determining the costs of river dikes leads to an underestimation compared to the costs in reality. In addition, hydraulic structures and future subsidence are not included, which will also lead to higher total costs. With these investments the flood risk will remain acceptable and the river dikes and dunes will continue to offer sufficient protection against floods with a total potential damage of 230 billion euros, consisting of 70 billion euros in economic damage, 20.000 casualties and 2,5 million affected persons.

In collaboration with the University of the Bahamas, we used the Charette model, the Three-point Approach and the conceptual framework: Build Back Better to propose a solution that involves several aspects: Reduced risk overall, increased social cohesion on the island, improved life quality and reduced costs during reconstruction in the aftermath of a hurricane event. Based on the analysis of the island, the hurricane and the important physical processes, a division between protection method is proposed based on the location on the island: collective and
individual protection.

Continuous sea level rise and growing environmental awareness have led to increasing implementation of nature-based solutions to counter coastal erosion. An example in the Netherlands is the Sand Engine---a mega-scale sand nourishment designed to feed the Dutch coast over a period of 20 years. For such designs to work, a good understanding of the governing natural processes is paramount. The behaviour of the sandy coast, however, is subject to natural variability in future weather and uncertainties in the interactions between sand dynamics and hydrodynamic forcing. To predict the evolution of coastal systems, engineers apply numerical models. Next to uncertainty due to variability in natural forcing, such models introduce a series of model-related uncertainties, which are often not consistently included in predictions. With limited knowledge of the magnitude of these uncertainties, the long-term strategy development and design of projects are impeded. Parameter uncertainty denotes our limited knowledge of the values of free model parameters and is an important source of overall model uncertainty. This study aims to quantify parameter uncertainty in process-based coastal area predictions by analysing uncertainty bounds for morphodynamic predictions of the Sand Engine. The analysis of parameter uncertainty is carried out for a study period of 14 months, from August 2011 (directly after construction of the Sand Engine) until October 2012. Using advanced numerical acceleration techniques, a synthetic dataset of 1024 morphological Delft3D predictions is generated, each with an identical hindcast period but different model parameter settings. First, a sensitivity analysis (elementary effects method) is performed to find the most influential parameters on three morphological indicators: cumulative volume change, shoreline position, and bed level change. Based on the sensitivity analysis, five parameters are selected for an uncertainty analysis. Subsequently, parameter uncertainty is quantified by the Generalised Likelihood Uncertainty Estimation (GLUE). To increase the convergence speed of the samples, quasi-random Sobol sampling is applied. To validate the applied parameter ranges and assess model performance, the predictions are compared to observations. Using GLUE, uncertainty bounds for the morphological indicators and posterior likelihood distributions of the five parameters are derived from the 1024 model runs. Finally, through a simplified uncertainty comparison, the relative influence of parameter uncertainty and wave climate variability is examined. A first key conclusion is that uncertainty in input parameters translates to significant uncertainty in predictions: cumulative erosion volumes for the peninsula show a spread of 1.3 -0.4/+0.7 million m3 after 14 months. Extended to bed level changes in 2D, the uncertainty bounds result in spatial uncertainty maps, which reveal that uncertainty is highest (5--6 $m$ spread) in the northern area of the peninsula, where a sand spit develops. Most uncertainty (90% for volume changes) develops in the first seven months, during which uncertainty growth correlates strongly to periods of high morphological activity (r > 0.95 for volume changes). Further, posterior likelihood distributions of the parameters indicate that, of the five selected parameters based on the sensitivity analysis, only three (f_sus, gamma, and d_50) significantly contribute to parameter induced uncertainty, while the other two (alpha_rol and theta_sd) are considerably less influential. This contrast in results is attributed to a resolution problem in the sensitivity analysis. Optimised parameter sets derived from the posterior likelihood distributions result in similar model skill as the best GLUE simulations (BSS = 0.8), implying that they may be close to the maximum achievable model skill within the examined parameter ranges. Finally, a simplified estimate of the variation due to wave climate variability is in the same order of magnitude as the parameter induced uncertainty bounds, implying that both uncertainty sources form significant contributions to overall prediction uncertainty. The presented results have an impact on two key levels. First, they can be used to communicate and address uncertainty in predictions of coastal change. For example, the spatial uncertainty maps can let stakeholders understand the potential range of outcomes for a certain design. Second, the results, combined with the created dataset, can provide valuable information for future morphodynamic studies. This work contributes to justifying the need for stochastic simulations, which are expected to be increasingly used for many coastal engineering and management purposes in the years to come.

With changing climatic conditions, droughts are expected to increase in duration and intensity. Under drying conditions, desiccation cracks can form in clay soil, which is often used as dyke cover and in some cases also for the core of the dyke. These desiccation cracks have a potential impact on the stability of dykes. The main objective of this study is to gain a better insight into the potential influence of desiccation cracks on the macro-stability of Dutch river dykes. With the help of PLAXIS 2D software, a numerical model is used to study the hydraulic response and stability of a dyke with desiccation cracks. It is chosen to simulate the effect of cracks by adjusting soil parameters of the cracked layer. Steady-state scenarios as well as time-dependent scenarios, where high water events are simulated, are studied. The influence of precipitation is also taken into account. For the steady-state case, a maximum decrease of the factor of safety of 5.6% is found. In the time-dependent scenarios, the factor of safety decreases up to 10.8% if a cracked zone with a depth of 2 meters is present. The magnitude of this decrease is mainly depending on the hydraulic conditions and the crack parameters chosen to simulate the effect of cracks. Both inner and outers slope failure is observed. The largest difference between the factor of safety of the cracked and the uncracked dyke occurs when the dyke fails due to outer slope instability as the factor of safety decreased most in the case of a rapid drawdown. From these results it follows that cracks can have a negative impact on the macro-stability of a dyke, but the difference is not unambiguous. Precaution is advised if significant cracks develop at dykes, but smaller cracks are not likely to lead to failure immediately.

The stability of breakwaters in seismically active areas is not always guaranteed. A new approach to model a breakwater subjected to an earthquake is with PM4Sand. The goal of this research is to find if breakwaters subjected to earthquakes can be correctly modelled with PM4Sand.
To investigate PM4Sand a breakwater subjected to an earthquake on centrifuge scale is modelled in Plaxis. The soils of the centrifuge test are modelled with PM4Sand and UBCSand. After calibrating the soil parameters and incorporating the proper earthquake signal results are generated and compared. The investigated results focus on the settlements of the caisson, deformations of the breakwater and generated Excess Pore Water Pressures underneath the breakwater due to the earthquake. Comparing the results from the numerical models with the centrifuge test result show that both the UBCSand model and PM4Sand can give comparable results for the settlements and deformations. However, both UBCSand and PM4Sand were not able to give the correct EPWP development underneath the breakwater.
Due to the incorrect behaviour of the EPWP underneath the breakwater resulting from the numerical models, this research is not able to conclude that PM4Sand can be used for modelling breakwaters subjected to earthquakes. Further research is needed to investigate the development of EPWP underneath the breakwater during an earthquake. Focus points of future research can be: the influence of the amplitude of an earthquake signal on the EPWP, the influence of modelling a centrifuge test on the behaviour of the EPWP and the influence of the initial static shear stress on the EPWP development.