The renewable energy sector is experiencing rapid growth, with offshore wind energy gaining significant global importance. Designing bottom-fixed offshore wind turbines (OWTs) with monopile (MP) foundations in seismic-prone regions, particularly in coarse-grained soils, presents challenges due to the risk of soil liquefaction during earthquake excitations. Current design practices for soil-structure interaction modelling address seismic pore pressure effects by accounting for the net decrease in soil shear modulus resulting from the development of excess pore water pressure.
This thesis examines the cyclic contour diagrams framework (CDF) for its capacity to predict excess pore water pressure (EPP) build-up in coarse-grained soils under seismic conditions. The framework is assessed by employing PM4Sand in PLAXIS2D to produce the cyclic contour diagrams for a coarse-grained material. This material is then used to perform site response analysis (SRA) on a soil column in PLAXIS2D. Subsequently, a total stress SRA is conducted using DEEPSOIL V7.0 to obtain the equivalent cyclic stress ratio (CSR) and the number of cycles by employing a best-match soil material similar to the one utilized in the PLAXIS analysis. By analyzing the cyclic stress history obtained from the SRA, the equivalent number of cycles and cyclic stress ratios are applied to the material's cyclic contour diagrams. Finally, the predictive capabilities of the method to predict the EPP calculated in the PLAXIS model are assessed.
Two case studies illustrate the framework's practical application. The first case focuses on Akita Port, Japan, which experienced significant damage during the 1983 Nihonkai-Chubu earthquake. The CDF was able to accurately predict liquefaction severity, validating the method. The second case study involves an offshore wind farm in the Netherlands, examining how liquefaction impact monopile foundation designs. The study highlights the importance of incorporating soil degradation because of liquefaction into the design of offshore wind turbines.
The findings indicate that the CDF is a viable tool for evaluating liquefaction potential in coarse-grained soils under seismic loading in engineering practice.

Hyperloop is a high-speed transportation mode that operates through magnetic levitation of so-called pods which are then transported through a tunnel in which a low-pressure environment is created. Due to reduced air resistance and friction, high velocities are achievable. This thesis addresses the behaviour of such a system operating at high velocities, focusing mainly on dynamic stability. The novelty of this study lies hereby in the implementation of a more realistic guideway model in the analysis. This was achieved by modelling the Hyperloop tube as an infinitely long cylindrical shell on a viscoelastic foundation from which the vehicle is suspended through an electromagnetic force, including an active control system.

This study aims to evaluate the system’s stability and its sensitivity to changes in the model by using mainly analytical methods which are supplemented by numerical computations where needed. There are two fundamentally different instability mechanisms studied, namely the electromagnetic instability caused by the inherent unstable nature of the suspension system and the wave-induced instability which originates from the energy feedback of radiated anomalous Doppler waves excited by the vehicle moving at large velocities. The research is motivated by two central questions: (1) What is the influence on the steady-state response when employing the more realistic guideway model? (2) What is the influence on the stability when employing such a model?

To address the first research question, only the steady-state of the guideway is analysed. Hereby, the electromagnetic force as well as the vehicle are disregarded and replaced by a constant moving load. To solve the system, the governing equations are projected on circumferential modes and transformed from space-time to the Laplace-wavenumber domain. This study analyses various scenarios based on their dispersion curves and/or steady-state response compared to a reference case.

For the second research question, the study analyses stability phenomena whereby the response of the guideway is expressed using a convolution of its Green’s function and the unknown electromagnetic force. Linearising the system around its steady-state equilibrium allows a computation and analysis of its eigenvalues which describe its stability. To complement and verify the analysis of the linearised system, a non-linear transient model is solved by using a numerical time-stepping algorithm.


The study highlights that the cylindrical shell model significantly affects the critical velocity, compared to an Euler Bernoulli beam model. Analysing the vehicle-structure interaction through the linearised stability analysis reveals stability concerns primarily driven by wave-induced instability when operating at supercritical velocities. In the subcritical regime, instability is only caused by the electromagnetic suspension, which can be overcome when choosing the right control parameters. To reduce the risk of instability it is advisable to choose the structural dimension such that the system operates at subcritical velocities to avoid the interaction between the two instability mechanisms.

This research advances the understanding of Hyperloop dynamics and its stability, providing a foundation for future studies and practical implementations aimed at developing the novel transportation mode.

The Hyperloop concept tackles the challenges conventional transport modes face, despite the considerable research gap. This research reduces the gap by focusing on the dynamic response of the periodically supported Hyperloop tube since the Hyperloop greatly exceeds the operational speed of traditional transport modes. Complexity is incorporated to obtain a detailed dynamic response using a finite element method. Progress has been made in incorporating the moving reference frame within the model with recommendations for the numerical stability of the transient analyses. Despite the computational inefficiency of the conventional non-moving reference frame, the model is utilised to conduct a parametric study. The study examines correlations between the stiffness properties of various Hyperloop elements, including the tube, rail, and the interface between the Hyperloop tube and column. These correlations are analyzed based on the system's response at the pod's location and the intersections between the tube segments. Here, the velocity of the pod is of paramount importance. Within the operational velocity range, only one critical velocity is identified, despite the system's infinite number of natural frequencies. The only dynamic amplification, identified as the main critical velocity, can be shifted beyond the operational range by increasing the overall structural stiffness. The shift can be realised due to the positive correlation with the main critical velocity and a negative correlation with the displacement difference at the interface between two tube segments relative to the structural stiffness. Within the research, the soil and pod interactions with the Hyperloop structure are excluded, leading to potential resonance with no risk of instability. The limitation can be addressed by modelling the pod as a mass-spring system and the soil as a two-dimensional medium. The files developed for the finite element models and the parametric study are available on GitHub (https://github.com/dedenner3/MasterThesis_Hyperloop). The files support reproducibility and further exploration of the methods described.

Hyperloop is a new high-speed transportation system currently in development. Utilising an electromagnetic suspension within a low-pressure tube, this approach eliminates the traditional wheel-track friction and drastically reduces the air resistance, targeting speeds up to 1000 km/h. Compared to traditional trains and aeroplanes, the Hyperloop is a more sustainable alternative as it produces no greenhouse gas emissions and uses ten times less energy than road and aviation transportation. The Hyperloop, therefore, has great potential to contribute to the goal of achieving climate neutrality by 2050.

Ensuring the stability of the Hyperloop is a critical challenge in its realisation. Multiple instability mechanisms are present in the system: (1) electromagnetic instability, (2) wave-induced instability, and (3) aeroelastic effects, such as galloping. Additionally, the imperfections in the guideway, make the Hyperloop system prone to parametric instability. This thesis primarily investigates how aeroelastic forces and parametric resonance interact with the electromagnetic and wave-induced instability mechanisms, impacting the overall stability of the Hyperloop system.

Based on the results, it can be concluded that the aeroelastic force destabilises the system, where its impact increases as the velocity rises. As the aeroelastic force continuously injects energy into the system, the unstable domain expands. Furthermore, parametric resonance, represented by ellipse-shaped indentations in the stability planes, is observed when the excitation frequency is twice the natural frequency of the system. Based on the control parameter range used for maglev trains, it is found that the stable domain is narrow, with only a small region prone to parametric resonance. Therefore, choosing the control parameters precisely is essential to prevent instability and parametric resonance.

When examining the combined effect of aeroelastic force and the irregular guideway profile, the results show that the aeroelastic force shifts the overall position of the stability boundaries but it does not affect the parametric resonance regions. Instead, the amplitude of the guideway’s irregular profile influences the size of the ellipses and the stable domain. A larger amplitude leads to an expansion of the unstable domain and an increase in the size of the ellipse; therefore, it is advised to maintain a smooth guideway.

This thesis further evaluates the capabilities of analytical expressions for the simpler 1.5 degree-of-freedom (DOF) electromagnetically suspended mass system by comparing it to systems that incorporate the beam dynamics. The results show that the analytical expressions from the 1.5 DOF system cannot approximate the position of the ellipses for the more complicated systems across all velocities. However, beyond the velocities of $1.3v_{cr}$, the analytical expressions effectively approximate the ellipse size. Notably, while the position and size of the ellipse are influenced by the guideway’s surface roughness amplitude, only the size of the ellipse is affected by the amplitude of the oscillations in the 1.5 DOF system. For the more complicated systems, the analytical expressions of the ellipse size relative to the amplitude provide accurate results, making the simplified system a valuable approach for estimating the ellipse size of parametric resonance in systems with beam dynamics.

Railway tracks are subjected to constant degradation in terms of geometry, and wear and tear of the track components (rails, sleepers, fasteners, trackbed layers, etc.). Over the years, trains have evolved immensely, but the track infrastructure has not kept pace. With rapid advancements in vehicle technologies, the design of rail infrastructure must cope with the challenges associated with the operation of railway tracks. In addition, railway transition zones (RTZs) degrade even faster (4-8 times) than normal tracks, leading to higher maintenance and operational costs. RTZs are areas where railway tracks cross stiffer structures (e.g., roads, bridges, culverts). The amplified degradation in RTZs is mainly attributed to abrupt changes in vertical stiffness and to differential settlement, resulting in amplified and non-uniformtrack responses. Even though the dynamic behavior of RTZs differs from that of normal tracks, the design of track components in these zones remains similar to normal tracks, with some modifications at the superstructure and/or substructure levels to mitigate the transition effects. There have been several attempts to mitigate the adverse effects of dynamic response amplification in RTZs, but they have proven either marginally effective or counterproductive. Therefore, a comprehensive design methodology for RTZs is needed that addresses the main degradation mechanisms leading to amplified degradation of these zones.

In this paper-based thesis, a novel methodology is proposed to design and evaluate railway transition zones. For this purpose, detailed analysis and design optimization is performed for a bridge-embankment transition using various two-dimensional and three-dimensional finite element models, different vehicle models, and surrogate models (using polynomial chaos expansion). Firstly, the proposed methodology establishes a robust design criterion to design and evaluate RTZs. The criterion relates the magnitude and uniformity (spatial and temporal) of the total strain energy in the trackbed layers to the permanent deformation of RTZs. This novel energy-based criterion is used to evaluate the most commonly used mitigationmeasures at the superstructure and substructure levels and to investigate the key phenomena governing RTZ design. Based on insights obtained from these analyses, a preliminary design of a novel transition structure called SHIELD (Safe Hull-Inspired Energy Limiting Design) is proposed. The second phase of the work is dedicated to identifying the most influential design parameters leading to optimized geometry of SHIELD and the desiredmaterial characteristics. The third phase involves the performance evaluation of optimized SHIELD subjected to critical loading conditions (e.g., critical and supercritical velocities, different directions of movement, hanging sleepers, non-straight rail) and SHIELD is shown to be a robust design solution for all conditions under study. In the end, the use of SHIELD is extended to another type of an embankment-bridge transition (with ballast running over the bridge) where it is shown to be equally (compared to embankment-bridge transition with no ballast layer over the bridge) efficient in mitigating the transition effects, and a laboratory experiment is designed to test the effectiveness of the proposed design criterion and methodology. A robust design methodology for RTZs is proposed in this work, which aims to minimize operation-induced degradation and can be adapted to different transition types and sitespecific conditions. A preliminary optimized design of SHIELD is proposed, which has been shown to be effective in mitigating dynamic amplifications in RTZs under both ideal and non-ideal conditions. The results and conclusions presented in this work demonstrate the promise of SHIELD as an intervention for railway transition zones, outline the next steps toward its practical implementation, and highlight the challenges that need to be addressed in future research.
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Underground tunnels are important infrastructures due to diverse applications in civil engineering. The dynamic behavior of the underground tunnels when exposed to seismic waves or the passage of high-speedmoving trains is of particular interest. Amplifications of displacements and stress concentrations may occur due to wave scattering and wave interference. Engineers concern about the vibration stability of moving trains as so-called anomalous Doppler waves may be generated when trains move at high speeds; the corresponding energy is fed into the vibration of the vehicle. Therefore, the traintrack- soil interaction should be properly considered to predict when the vehicle vibration becomes unstable. This thesis aims to present a semi-analytical solution for the response of a half-space with an embedded tunnel subject to seismic waves and to analyse the vibration stability of high-speed trainsmoving through that underground tunnel. Previous studies indicate that the method of conformal mapping is a promising analytical method to solve the two-dimensional (2D) wave scattering problem due to its computational efficiency and accuracy. Thus, the first objective of this thesis is to extend the method of conformal mapping to three-dimensional (3D) case and systematically evaluate its performance. Results reveal that inaccurate results maybe obtained, particularly at high frequencies. This observation motivates the second objective of this thesis, which focuses on verifying the accuracy of the specific application of the method of conformal mapping in which thewaves scattered fromthe half-space surface are represented by cylindricalwaves that originate from an image source of a priori unknown intensity. To this end, a simpler 2D model is considered, involving a cylindrical cavity embedded in an elastic half-space subject to a harmonic anti-plane shear wave. The performance of the indirect Boundary Element Method (indirect BEM) is evaluated too for this model in view of the choice of the appropriate solution method for the second type of dynamic problem considered in this thesis. For this second type of dynamic problem, due to the identified inaccuracies at high frequencies for the 3D problem, the indirect BEM is utilised to investigate the stability of vibrations of an oscillator moving at high speeds through a tunnel embedded in soft soil, which is the third objective of this thesis… @en

In transition zones, railway tracks experience significant inhomogeneity in their mechanical properties—more specifically in vertical stiffness. In such areas, conventional tracks (soft tracks) are typically encountered with other engineering structures with noticeably larger stiffness, such as bridges and culverts (stiff tracks). This inhomogeneity together with the passage of high-speed trains leads to amplification in dynamic response, which in turn results in faster degradation and higher cost of maintenance at transition zones. In practice, various mitigation measures have been adopted which have led to improvement in track performance to a certain degree.

This thesis is mainly focused on the feasibility of using the tuned mass damper (TMD), as a novel mitigation measure, for improving the aforementioned undesired behavior. Additionally, the efficiency of two already existing corrective measures, namely auxiliary rail and under sleeper pad (USP), is investigated at transition zone.

The track is modeled as an infinite one-dimensional Euler-Bernoulli beam resting on a piecewise-homogeneous and continuously distributed Kelvin foundation. For each mitigation measure, semi-analytical solutions are derived through the Fourier transform method. Regarding TMD analysis, mechanical parameters are optimized by an evolutionary algorithm (NSGA-II), in which the discrepancy between the soft and the stiff tracks’ wavenumbers is minimized. In regard to auxiliary rail, two configurations with multiple number of extra rails (ERs) are evaluated; ERs over soft track only, and ERs over all domains. Additionally, USPs with different stiffness are considered for their arrangement along the track. The efficiency corresponding to each mitigation measure is mainly evaluated through dynamic amplification factor (DAF) and power input.

The system with TMD demonstrates a significant reduction in DAF amplitude corresponding to the load velocity for which the optimization is performed. This improvement is also evident for velocities close to the aforementioned load speed. In fact, the addition of TMD results in presence of a free propagating wave behind the load and decreasing the critical velocity in the corresponding system. The outcomes corresponding to power input suggest a significant reduction in potential damage to the foundation due to the employment of TMD.

Furthermore, the application of ER leads to improvement in dynamic performance of the track by increasing the critical velocity to a larger value, at which the corresponding DAF indicates no reduction. In addition, considering more than one ER along the track does not lead to a noticeably better result compared to when only one ER is added. Moreover, applying ER over soft track leads to inhomogeneity in bending stiffness and mass corresponding to the beam element at transition point. Therefore, the system with ER over all domains indicates a better dynamic behavior. Potentially, less damage to the foundation can be signified in the system with ER according to the power input response.

Finally, USP can significantly affect the equivalent stiffness of the track. It is concluded that the efficiency of USPs in mitigating the amplified response is strongly dependent on their stiffness and arrangement along the track, as well as the stiffness variation in the supporting structure; improper design of USPs alignment can adversely result in even more amplified responses.

In the Netherlands, there is an increasing need to create residential spaces in its already crowded cities to accommodate the growing population. Constructing high-rise buildings is one way to try to solve the issue. However, high-rise buildings are sensitive to wind-induced vibrations. The accurate prediction of the dynamic response is important in high-rise building design. In building design practice, calculating the dynamic response of high-rise buildings under wind loading typically involves simplifying the structure as a single degree of freedom system, characterised by the first eigenmode properties and subjected to a white noise spectrum. The damping and natural frequency of the building substantially impact its dynamic response. These parameters are challenging to predict with accuracy. Additionally, in the presence of soft soils, soil-structure interaction can play an important role in energy dissipation and influence the structure's natural frequency. In practice, soil-structure interaction is either disregarded or simplified.
In order to assess the effect of soil-structure interaction on the dynamic response of the building, this study models in a robust manner: the foundation, the tower structure, and the wind load. This newly developed model is addressed as the HF model. The investigation consists of a case study and a parametric study. Additionally, this study compares the predictions by the newly developed model with those obtained with a model as specified in the Eurocode. The case study provides a comparison between the models and the measured dynamic response of the New Orleans Tower. The parametric study looks into the influence of soil stiffness and material damping on the dynamic response of high-rise buildings. Furthermore, it investigates how these parameters affect the dynamic response of structures with various slenderness ratios.
The case study was used to demonstrate that the developed model accurately predicts the measured dynamic response of the New Orleans Tower in the along-wind direction. For all the examined dynamic properties, the error compared with the measurements was lower than 7%. In the case of the Eurocode model, the results demonstrate that, when using the natural frequency estimation recommended by the Eurocode, it provides a 30%–35% underestimation of the peak acceleration compared to measurements. This Eurocode model overestimates the natural frequency and overall damping, which causes it to underestimate peak acceleration. However, the natural frequency determined in the design phase of the New Orleans Tower was significantly lower than the value obtained with the recommended estimation method in the Eurocode. With this lower natural frequency, the peak acceleration is overestimated by around 50%. This underestimation of the natural frequency and overestimation of the damping provided acceptable conservative results. Although this showcases the importance of accurate predictions of both natural frequency and damping, having poor predictions that cancel out each other’s effects is not desirable.
The results from the parametric study support the findings from the case study. This shows that the case study’s findings apply to the more extensive range of building configurations investigated in the parametric study. In general, the Eurocode model, for slender structures on soft soil, overestimates the natural frequency and overall damping, which causes it to underestimate peak acceleration.
The parametric study revealed that the building's first natural frequency and global damping ratio are significantly influenced by the soil stiffness and soil material damping, which can result in various effects on the peak acceleration. In the case of soil material damping, not considering it at all or considering a higher value could lead to 20% overestimation and 40% underestimation of peak acceleration, respectively. Soil stiffness had more intricate effects since it affected the natural frequency and the amount of energy dissipated by the soil radiation damping, the soil material damping and the structure material damping. For particular combinations of parameters, soil stiffness had up to a 40% increase in the peak accelerations compared to the fixed foundation.
The results of this research show that the soil stiffness and soil material damping, for the ranges of properties relevant to the Netherlands, significantly influence the accurate predictions of the wind-induced dynamic response of high-rise buildings. Especially, there was found a higher influence on the dynamic response for the extreme cases of high slenderness ratio structures on very soft soils.

The Hyperloop is a high-speed means of transport, consisting of a bullet-shape vehicle travelling in a quasi-vacuum tube, electrically powered and moving through an electromagnetic levitating system. This allows the reduction of air resistance and wheel-rail contact friction, which translates in higher speeds for smaller power inputs. In the Netherlands, the Dutch company Hardt Hyperloop, has developed a new design concept of such technology, by means of electromagnetic suspension systems, unlike the most commonly applied levitating techniques.

The main aim of this project is to investigate the stability of the electromagnetic suspension levitation system, study the effect that the implementation of an error-based closed-loop control system has on the system dynamics and investigate the vehicle-structure interaction once a control system has been applied to the system.

Along these lines, the overall infrastructure-vehicle system is modelled through an equivalent two degrees of freedom system. In this manner, the inherent instability of the electromagnetic system is confirmed and the initial vehicle dynamics are highlighted. Afterwards, an error-based closed-loop PD-control system that applies to the system definition and reacts on the uncontrolled system dynamics is implemented and the effect of the control parameters on the dynamics and the stability of the system is studied. A certain stability region in the parametric space is derived, which ensures the stability of the system for significant perturbations of the vehicle from its equilibrium point. Besides, the existence of a subcritical bifurcation with respect to the parameter combination is demonstrated. The safety margin in the time delay of the controller response is studied, so as to define a slack time that accounts for not only processing and sampling delays, but also unforeseen events. Finally, the vehicle-infrastructure interaction is studied and its stability is ensured, by means of the previously defined control scheme.

The stability analysis of electromagnetic suspension system applied to Hyperloop in simplified two degrees of freedom system has been studied deeply where the track-beam is regarded as a point mass and the effects of velocity and beam are neglected. However, there is little reference on the study of the interaction between electromagnetic suspension system and wave effects.

The main aim of this thesis is to investigate the dynamic behavior of the EMS vehicle-beam coupled system using the one-dimensional model, and illustrate the combined effects of the EMS and guideway on the vehicle instability at different horizontal velocity by comparing with results of EMS system in simplified model and mechanical system in one-dimensional model.

Along these lines, the tube is modelled as an infinite long Euler-Bernoulli beam resting on a homogenous viscoelastic foundation and the vehicle is modelled as a point mass. The response of the system is obtained both numerically and analytically. The values of control gains are determined based on the equivalent simplified two degrees of freedom EMS system. A representative mechanical system is designed to show the anomalous Doppler waves effects. It is found that for inappropriate values of control gains which will cause instability of vehicle at static state, the one-dimensional guideway has positive effects which can stabilize the vehicle at certain range of subcritical velocity, whereas for appropriate values of control gains the EMS system can counteract the wave-induced instability and keeps the vehicle stable at even supercritical velocity. Finally, a method to linearize the system is presented which allows eigenvalue analysis.

The instability of a moving mass / oscillator due to surpassing the velocity of the minimum group wave velocity (in a continuous homogeneous structure) has been studied extensively and is well understood. In contrary to that, Parametric Instability of a moving mass / oscillator on a continuous periodic structure has been studied less extensive and therefore the mechanism behind the instability is unknown. Literature that is avaiable on this topic mainly focuses on continuous periodic inhomogeneous structures, namely where the foundation is modeled as a continuous periodic inhomogeneous structure. Even less well studied are models where instead of a continuous periodic inhomogeneous foundation discrete periodic supports have been used. So far as known to the author there has also been no studies where the discrete supports are coupled through a medium. In order to solve the transition curves discerning the stable and unstable domains concerning the parametric instability of a moving mass / oscillator the analogy with the Mathieu equation is used, which tells us that the solution on those transition curves will be periodic with once or twice the period of the parametric excitation. In this thesis we have focussed on studying the use of the analogy on continuous structures founded upon periodic supports.

The Mathieu equation describes the motion of a parametric oscillator, for example a pendulum with a length that periodically varies over time. The theory that predicts the solution to the Mathieu equation is called Floquet theory and ascociated with the solution are the Floquet exponents, these exponents dictate whether the solution will be periodic and bounded or unbounded. By solving for the Floquet exponents of the Mathieu one sees that for an increase of the amplitude of the parametric excitation the system will experience a greater exponential growth. For a greater mistuning between the parametric excitation and the natural frequency of the equivalent non-parametrically forced equation we see that the system will experience a smaller exponential growth. Outside the instability domains the solutions will be bounded and periodic and contain a wide variety of frequencies. When damping is introduced, the value of the damping coefficient (if written in the canonical form of a viscously damped single degree of freedom equation) will be subtracted from the value of the undamped Floquet exponents and by that result in an upward shift and narrowing of the transition curves. Furthermore, outside the instability domains we will see two regions: the first lies close the the transition curves and is asymptotically stable with a period equal to that of the transition curve, the second covers the remaining stable region and is asymptotically stable and periodic with a wide variety of frequencies.

Regarding the Parametric Instability of a moving mass / oscillator we have studied three different models: a continuous Euler-Bernoulli beam on periodic spring supports, a continuous Euler-Bernoulli beam on periodic supports that are complex (i.e. modeled as an oscillator between two springs), and a continuous Euler-Bernoulli beam on periodic supports that are founded upon a 2-dimensional lattice. Of these models we have conducted a parametric study as to study what the effects are of the various parameters. We have seen that whenever the ratio between the stiffness of the supports and that of the beam is increased, the instability domains will shift to higher velocities and become wider. For certain combinations also 'islands' of instability may appear, where these 'islands' indicate stable areas between regions of instability. If damping is introduced into the system, this will generally narrow the instability domains and shift them to higher values of the mass and lower values of the velocity. However, for certain parameter combinations adding damping will lead to a widening of the instability domain. In the case of a moving oscillator the instability domains will narrow and be shifted to lower values. If the support is modeled with a mass it will affect the general trend of the transition curves through its own resonance, hence for a complex structure it is advised to model the supports with the correct dynamic equations. Last but not least, if the supports are coupled through a medium (a 2-dimensional lattice in this case) one will generally see a similar effect as adding damping has.

In this thesis we have also studied three real world cases: a regular railway track, a high-speed railway slab-track, and the Hyperloop. In the first case we have seen that Parametric Instability will most likely have no influence. For the slab-track, being much more stiff, Parametric Instability will be important. However, a more extensive study with several cases must confirm this. In the last case, namely the Hyperloop, we have seen that for a moving mass the instability domains are relatively large as compared with the other cases. We have also studied the Parametric Instability of a test-pod, which showed that its instability domains that are negligible. Of course, this was merely a test-pod not capable of transporting people, hence when a larger pod is studied it may be expected that the instability domains may not be neglected.

An important subject in the research on the behaviour of railway structures is the validation of numerical models by means of in-track measurements. Many forms of track measurements have taken place all over the world, mainly in the sense of strain and acceleration measurements, but a more unexplored area is that of the direct measurement of stresses in the ballast.
The aim of this research is to find the best way to equip a railway sleeper with measuring instruments in order to use it for validation of computational models. The sleeper must be able to measure the the vertical velocity of the sleeper as well as the normal stresses on the ballast-sleeper interface over time.

In order to predict the quantities to be measured, a finite element model was build for this research with the Kratos open source software package. The model comprises one single sleeper on top of a volume of ballast, both in solid elements. A dynamic load was applied vertically on top of the sleeper to simulate the passing of a double axle bogie. Linear elastic springs were fixed on top of the sleeper to represent force of the rail pulling the sleeper back to its initial place.
In order to analyse the effect of hanging sleepers, interface elements were used in between the ballast and the sleeper to simulate hanging gaps. The idea is that these elements transfer no stresses when the surfaces are physically separated, and adopt Mohr-Coulomb criteria as soon as the surfaces approach each other. This method turned out to be very difficult to implement, despite numerous discussion with the software engineer it was not possible to script this in the FE software in such a way that all calculations converged without any errors.
During the modelling of the sleeper, it was found that the forces on the sleeper are highly dependent on the resistance of the rail. The rails have such a high bending stiffness that they hardly show any curvature over the length of only a few meters, so the sag of the rail is mainly dependent on the behavior of the surrounding sleepers. It was concluded that, to get a good picture of the behaviour, it is not sufficient to model only one individual sleeper, but it is necessary to look at a larger part of the railway track in order to involve the coupling between the sleepers.
The results from the computational model were used to determine the magnitude range and the frequency domain of the values to be measured, in order to be able to select the right measuring instruments. The results were also used to select the right positions for the sensors on the sleeper. Due to the constraints described above, a certain margin of uncertainty has been adopted.

The vertical speed of the sleeper is best measured with accelerometers, the large amount of previous applications of this type of measurement has shown that this measurement works well and will not lead to problems.
It was considered to use pressure cells for the measurement of interface stresses, though this device turned out to be difficult to fix at the sleeper and it gives very little information on the distribution of stresses. It was concluded that the best way to measure the ballast-sleeper interface stresses is by using the matrix based tensile surface sensor (MBTSS). This instrument is able to capture the stress distribution on a surface over time, by measuring the electrical current flow through a matrix of conductive lines, the current is resisted when certain forces are applied on the surface. Tekscan is a manufacturer that offers a wide range of MBTSS types, including sensors previously used in railway measurements. A certain protection will be needed to protect the sensor from being damaged by the ballast particles.
Previous applications of MBTSS in railway structures showed the calibration of the sensor to be very difficult. This presumably has to do with the way the stresses are distributed over the sensor surface. Since the stresses of the ballast are often compressed to very small contact points, it should be made sure the stresses will not get lost between the sensels, that are the points on the surface where the stress magnitudes are measured. The advice is to cover the MBTSS with an under sleeper pad, this is a relatively stiff mat that, in addition to offering protection to the sensors, also spreads the ballast forces. Laboratory tests will have to be performed in advance of the field measurement to test whether a correct calibration is possible. It can not be made sure that a fully successful calibration method will be found and therefor additional measurements are recommended for a validation for the stress magnitudes. A first validation can be found by equating the sum of the vertical forces with the mass times the acceleration of the sleeper. To find the sum of the vertical forces, the load on top of the sleeper at the rail-sleeper connection, has to be measured as well. This can be realized by placing MBTSS between the baseplate of the rail and the sleeper. Similar measurements described in literature proved this type of measurement to be feasible. Furthermore, the result of the acceleration measurement will have to be used here as well. A second validation can be performed by determining the moment distribution over the length of the sleeper, this can be conformed to the magnitude and distribution of the vertical stresses on the sleeper. The most reliable way to perform this validation is by using fiber measurements to find the moment distribution over the whole of the length. The most important positions over the length of the sleeper are under the rails and in the middle of the sleeper, because the peaks in the moment distribution are expected here based on the computational model calculations.

The offshore wind industry is a quickly growing market because the increasing demand for clean energy sources. Large wind speeds and the abundance of potential wind farm locations make Offshore Wind Turbines an interesting solution. Because of high continuous dynamic loading and extreme environmental conditions, the structural design requires a detailed assessment, especially in the Fatigue Limit State. In this thesis, the focus lies on improving the modeling of monopile foundations for Offshore Wind Turbines, which could pave the way towards more efficient foundation design.

The conventional method of modeling the monopile foundation of an Offshore Wind Turbine is with a nonlinear elastic distributed spring stiffness along the monopile (using p-y curves). Damping related to the soil is considered through either global damping (like Rayleigh damping) or local viscous damping. However, the response of the soil around the monopile under wind and wave loading is better described through a nonlinear hysteretic (rate-independent) model, which is computationally demanding to model in the time domain. Next to that, a conventional frequency domain method can not be combined with any nonlinearity. Therefore, linear elastic models are used to model the soil response in frequency-domain simulations.

The goal of this thesis is to combine a nonlinear hysteretic soil model with a frequency-domain analysis. A response amplitude-dependent linearization of the nonlinear hysteretic element is made. The combination of the response amplitude-dependent element with an iterative solution strategy, the Equivalent Linear method, is shown to approximate a nonlinear time-integration under both harmonic and multiharmonic loading, as long as the nonlinearity is limited.

A nonlinear hysteretic model is fit to available soil reaction data and a response amplitude-dependent linearization is generated. A Finite Element model that can be combined with the Equivalent Linear method is set up and verified with a case study structural model of an Offshore Wind Turbine. The model is subjected to (high) Fatigue Limit State wave loading. The results are compared to both a conventional frequency-domain method (with a linear elastic small-strain soil model) and a nonlinear time-domain method (with a nonlinear elastic soil model). The deflections and deflection spectra in the foundation found through the Equivalent Linear method correspond to results from the nonlinear time-domain method, provided the influence of higher harmonics is limited and the response has a similar amplitude throughout the analyzed time window.

Results from the Equivalent Linear method show that the main frequency of the first resonance peak is around 2% smaller than the first natural frequency of the system, which is consistent with the results found through the nonlinear time-domain method. The identified soil damping in the first mode is 0.64-0.8% critical (4-5% log. dec.), which is similar to other literature. By combining observed system properties with literature about fatigue damage estimation, a hypothesis is stated: the fatigue damage in the foundation calculated through an Equivalent Linear method with a nonlinear hysteretic soil model will be lower than the fatigue damage calculated through a nonlinear time-domain method with a nonlinear elastic soil model.

Areas of railways with considerable variation of track properties encountered near structures such as bridges and tunnels are referred to as transition zones. Degradation rates at these transition zones are higher compared to the remaining railways. These high degradation rates result in high maintenance expenses. In order to come up with solutions that reduce this degradation and thus also the expenses it is needed to have an understanding of the underlying mechanisms in the railway tracks. This is done by formulating a mathematical model of the railway track which can then be analyzed. Researchers have been using different models for this purpose.

The choice is often made to model the railway track an elastically supported beam. This elastic foundation represents the supporting structure of the railway tracks and its stiffness is based on static load cases. This 1D model is often used due to its relative simplicity compared to other more complicated multidimensional models. This model has been thoroughly analyzed and it has turned out to have an important constraint which is its inability to result in a critical velocity that makes sense for railway tracks. The critical velocity of a railway track is that velocity at which waves travel near the surface of the subsoil of the supporting structure. A vehicle that moves with a velocity close to the critical velocity of the railway track causes a strong amplification of the response. Another important constraint of this model is the fact that there is no possibility to directly adjust the stiffness properties of the different components of which the railway track exists individually.

It is opted in this thesis to adjust the previously mentioned 1D model by the addition of a distributed mass and an extra elastic layer. The upper elastic layer represents the pads and the lower elastic layer represents the remaining of the supporting structure. The idea behind the addition of the distributed mass is to include the activated mass of the supporting structure by the moving load. This is done in order to take the dynamical behavior of the supporting structure into account and thus obtain realistic critical velocities. The idea behind the addition of an elastic layer is that it enables to adjust the stiffness of the pads individually. By using this model one can thus modify the stiffness of the pads at transition zones and study whether it is possible to decrease the degradation which is the initial goal of all studies on transition zones.

In this thesis the adjusted model is analyzed thoroughly for different physical phenomena. Such analyses cannot be found in the literature, to the best of the authors knowledge. The system response has been investigated for a uniformly moving load of a constant magnitude. This has been done for homogeneous properties of the elastic layers and for an abrupt jump in the stiffness of the lower layer. Attention has been given to both the displacement fields of the rails and energy propagation in the system. Also a numerical model has been formulated for other load cases and stiffness properties. In order to simulate infinite system behavior non-reflective boundary conditions have been derived and applied to the numerical model. It has been found that indeed a far more realistic critical velocity can be obtained by making use of the adjusted model. It has furthermore turned out that the system response at a transition zone are very similar for both models for the same ratio of load velocity to the critical velocity. The adjusted model has been investigated extensively in this thesis and it can thus be used as a reference work for future researchers that wish to apply the model. The research that should be performed next in the authors view is to investigate the possibility of reducing the degradation at transition zones by adjusting the stiffness of the pads.

A new form of high-speed transportation, which involves a magnetically levitated vehicle that travels through a vacuum tube, is currently under development. Those parts of the trajectory along which the tube is supported by columns---which possess both axial and bending stiffness---requires the use of a model that allows to study a form of instability that is inherent to this type of support. Specifically, the stability is studied of a point mass with a lateral and vertical degree-of-freedom that moves with constant velocity along an infinite Euler-Bernoulli beam on coupled lateral-vertical periodically inhomogeneous foundation. The beam model is able to deflect in both the lateral and vertical direction and the concentrated mass is attached to this beam by a lateral and vertical contact spring. With the help of a perturbation method it is shown that the system's vibrations can become unstable. As for the model that only exhibits degrees-of-freedom in the vertical direction, the underlying physical phenomenon is parametric resonance, which occurs because of the periodic variation of the foundation stiffnesses. For the lateral-vertical model, this form of instability is referred to as combination parametric resonance, which yields four instability domains in the velocity-mass parameter space as opposed to the one domain for the vertical-only model. The center lines of these four domains depend strongly on the period of inhomogeneity; the larger the period, the higher the velocity at which instability occurs. Vehicle-structure interaction (i.e. the maglev system) also affects the center lines considerably; including contact springs between the beam and the point mass reduces the velocity at which instability occurs. To obtain the complete instability domains and to be able to investigate the mitigating effect of foundation damping, the method from another paper is recommended to be used for follow-up research.

In the design of offshore wind turbine generator (WTG) support structures, a large number of environmental parameters are used. The most important ones include the wind climate (wind speed and wind direction probability distributions), the wave climate (wave height and wave direction as well as peak frequencies of the waves, and water levels) and the soil conditions. These data in combination with the operational data of the wind turbine, such as the rotor speeds, pitch angle and yaw angle are used in dynamic simulations to determine the loads on the structure. Combining all these data correctly ensures that the support structure design, which is subject to large dynamic loads, is fitting for each specific location of the WTG. In particular, the environmental conditions should not coincide too much/often with the support structure natural frequencies, as that may result in resonance, thereby increasing fatigue life consumption. The dynamic behavior of these offshore support structures is of eminent importance. During the operation of WTGs, the actual dynamical properties of the WTG can be compared to the design. There are several reasons behind the goal of this comparison, for example verifying if the loading assumptions in the design were correct, assessing whether the life time can be extended or even whether the structure can be optimized (e.g. better foundations). Typically, this is done by comparing acceleration measurements of the WTG during idling (e.g. non-operational) conditions and applying Operational Modal Analysis algorithms. Given the high availability of modern wind turbines (e.g. >95% of time in operation) such measurements cannot be done as often as desired for this purpose. Therefore, the question arises to what extent the dynamical properties of WTGs can be estimated using measurement data obtained during operational (operational) conditions. This research explores the applicability of OMA algorithms in estimating the dynamical properties: the natural frequencies, the mode shapes and modal damping for operational conditions of offshore wind turbines on monopile foundations, using the Luchterduinen offshore wind park as a case study. The OMA technique explored in this thesis is Eigensystem Realization Algorithm. Test cases were used to confirm the performance of ERA for the estimation of the dynamic parameters. Stability diagrams were used to identify poles for stable modes (frequencies) in the frequency spectrum of data samples and to estimate a correct size of the Hankel matrices. It is concluded that this preprocessing and pre-analysis of the results is important to confirm the performance of ERA to correctly identify stable modes of support structures of operational offshore WTGs.Overall, it is concluded that ERA can yield useful results in estimating the natural frequencies for both ON and OFF, provided that an automated analysis is combined with a visual analysis. Even then, the accuracy and the consistency of the identified frequencies is moderate. ERA does not perform well for estimating the mode shapes, yielding inaccurate and inconsistent results. Based on the results of this work, ERA is found not to be capable of estimating modal damping ratios. The consistency for the mode shapes is not in all cases good and further study is recommended for both the mode shapes and the modal damping ratio. Another recommendation is to further study the size of Hankel matrices for this application. Furthermore, it is advised to also investigate the use of more advanced Operational Modal Analysis algorithms. The results of this study may be used to explore differences between wind turbines with and without scour protection and also to compare identified dynamic parameters to values used in the design.

As the exploration for oil and gas is shifting towards greater water depths, there is a market for subsea rock installation (SRI) at these large water depths as well. Boskalis is a key player in the rock installation market and installing rock material at water depths of approximately 3000 meters is still far from routine work. Therefore, Boskalis is researching accurate and cost-efficient systems for installing rocks in these ultra-deep waters.
Since this is a concept with operations that are not applied before by Boskalis, there are no structural test data available that could be used for research purposes. Therefore, it is decided to perform scaled model tests to obtain reliable production rates of the rock installation process. The basket and its corresponding release mechanisms is built on scale and forces are measured during the release process for different configurations, where the type of release mechanisms and the area of opening were varied. The production rates that followed from these force measurements are used as input parameter in the model that simulates the dynamic response of the envisaged concept.
In order to better understand the force and motion behaviour of this envisaged concept, a simplified one-dimensional cable model has been constructed in Matlab to simulate the dynamic response of the lifting wire and basket, and the force distribution in the lifting wire.

A railway turnout, which is a combination of a switch and a crossing is an important component in the railway network to divert trains. Due to the change in contact between the wheels and the rails as the train negotiates a turnout, severe impact loading occurs in two-directions: vertically and laterally. These cause negative environmental impacts in terms of ground vibrations. Therefore, understanding the ground response due to a railway turnout qualitatively and quantitatively is essential for soil surface in the vicinity. This thesis focuses on qualitatively and quantitatively describing the ground response through a dual load model setup through semi-analytical approach. A two-dimensional load on an Euler Bernoulli beam which is placed on a three-dimensional half-space is considered to describe the ground response. Followed by which, a load spectrum defining the interaction between the wheels and the rails is considered and the ground response is analysed. Measurements from the vicinity of a turnout is also analysed in order to compare the performance of the model to that of the real-life scenario. It is further concluded that qualitatively the ground response caused due to impact like loading that occurs at a crossing, and the presence of lateral loading is able to be explained by the model. Quantitatively, to analyse the response recommendations are to be followed to acquire the accurate load spectrum along with considering the complex track geometry for the lateral loading.

Railways and other sources of environmentally induced vibrations often lead to annoyance and sometimes property damage. In this framework, transition zones are deemed as the most sensitive locations on the railway track, especially to high vibrations and impact loads. This causes high maintenance costs and is often very annoying, as the availability of the track gets limited during maintenance processes. One of the main reasons of this problem is the stiffness change of the railway supporting structure which is sometimes abrupt. This thesis will shed some light on the factors playing roles in altering the vibration intensities in level crossings. Moreover, the effects of these factors on ground vibrations will be highlighted. Further on, a model is presented which incorporates all these parameters. This model can be used to predict the change in ground vibrations in level crossings. The objective of this thesis is to determine the influential parameters in terms of the response vibrations in the surroundings of railway tracks. On that account, following an in-depth literature study, and based on the analysis of the measurements performed at Movares, it was suggested to investigate three factors being the ambient temperature effect, the hanging sleeper scenario and the inhomogeneity of foundation and analyze their impacts. The in-situ measurements illustrated a correlation with temperature, where the vibrations are amplified during hot periods and in the summer season. Besides that, the reports indicated the presence of the hanging sleeper scenario, where the suspension between the rails and the foundation is no longer active. It was also reported that locations with inhomogeneous foundations experience higher vibrations than those with quasi-homogeneous foundations. On those grounds, it was decided to study the effects of the hanging sleeper scenario, the ambient temperature and the presence of a slab-track crossing on the track. A complete vehicle/track/soil numerical model has been used in the parametric study in order to assess the factors affecting the response vibrations induced by trains and to quantify their impacts. Along with that, the numerical results have been validated, to some extent, with analytical results. More specifically, the steady-state response obtained with both approaches are compared present a good agreement. The results exhibit that the hanging sleeper phenomenon has a substantial effect on the vibrations. Furthermore, the existence of a level crossing (representing a foundation inhomogeneity) proved to be of significance as well. Lastly, the ambient temperature possesses a limited impact which could turn severe in extreme conditions.

This thesis aims to gain insight into the global dynamic fluid-structure interaction response of a submerged floating tunnel (SFT) under the wave and current loading to enhance the design. To this end, the tunnel tube is modelled as a Euler-Bernoulli beam deformed in three directions (horizontal displacement, vertical displacement, rotational angle), the discrete anchoring system as a continuous elastic foundation considering geometrical nonlinearity. Then, the Morison equation is used to model the combined current and wave loading and the oblique wave loading. A simplified wake oscillator and a non-simplified wake oscillator are used to model the vortex-induced vibration (VIV) under current loading. Subsequently, the modal superposition method and Runge-Kutta method are applied to obtain the response of the SFT in the time domain. The Fourier transform and the wavelet transform are applied to the time domain signal to perform a frequency domain analysis. Finally, a test on a scaled SFT model is used for a case study. A parametric study is carried out based on the results to study the influence of the geometrical and structural design parameters. The results show that the motions in the horizontal direction and the rotational direction are significantly coupled together. Geometrical nonlinearity introduces the second-order effect to the system leading to a complicated vertical motion with a considerably larger displacement compared with the linear case. The amplitude of the VIV on the tunnel tube of the scaled model is very small based on the non-simplified wake oscillator. Moreover, it is found that, basically, increase of the BWR, increase of the stiffness in the cables, increase of the distribution of the net buoyancy in inclined cable, decrease of the tunnel length or decrease of the inclination of the inclined cables can reduce the maximum response of the SFT. Based on the above findings, it is concluded that a global dynamic analysis is suggested when a SFT is expected to be subjected to oblique wave loadings. Geometrical nonlinearity is necessary to be considered for an accurate analysis especially for the response in the vertical direction. It is also necessary to be considered when the influence of the BWR is of interest. The VIV on the tunnel tube is negligible base on the scaled model.