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Wind energy is one of the most promising sources of renewable energy worldwide. Its utilization has substantially increased for the last decades, both onshore and offshore. Offshore wind energy will have a lot to offer within the following decades, thus their foundations need to be prepared. Some of the current wind farms and wind turbines are now reaching their lifespan and, the turbines’ market is developing itself so rapidly that current turbines are getting behind the times with tremendous ease. It is here where the scope of this Master Thesis comes: what shall we do? Should we dismantle wind farms when they reach their lifespan, or should we maybe try to give them a further use? Accommodating for a new a larger wind turbine will need to account for new and higher climate actions and loads, namely winds, waves, ocean currents, the water level variation and the always difficult to predict ice actions. What is aimed in this Master Thesis is to set the basis for a procedure to dimension and define feasible solutions for the offshore wind turbines Gravity-Based Foundations to be expanded, avoiding the necessity of replacing them completely, with the environmental and economic benefits this would have. As this could turn to be an unmanageable problem to be solved, a Case Study where details can be set is performed at the Lillgrund Wind Farm site, in the south-west coast of Sweden, in the Öresund that separates Copenhagen and Malmö. A thorough description of the climatic actions and surrounding aspects is performed, while always dealing with uncertainties. With all that information, an analytical stability analysis is performed to account for three failure modes, namely: sliding, tilting andground failure. Additionally, a numerical FE-model is carried out in ANSYS in the aim of assessing the stresses and deformations that this kind of structure will suffer. Four alternatives are evaluated, and their behaviour is assessed based on the new external design actions. Analytical results show stability difficulties in two of the geometries inspected, while assure it in the other two. The FE-analyses show high concentrations of stresses on the GBS shaft, while model affordable deformations under the load combinations inspected. These results are also compared and contrasted in between them, and sensitivity analyses for the FE-models are performed in order to assure their good behaviour and development, and the trustworthiness ofthe results found. Based on these results, some conclusions are drawn from the developed processes. The main finding is the width and weight dependence of the solution, as well as the shape and dimensions. Future research needs such as scouring effects are finally accounted for necessary inspection to be made as continuation of the work here presented.

After only two years of service, extensive cracking was found in the webs of two light-rail commuter line bridges in Stockholm, the Gröndal and Alvik bridges. Due to this incident it was found necessary to study the means available for analysing shear cracking in concrete structures subjected to in-plane stresses. The aim of this PhD project is to study shear cracking with these two bridges as reference. In this thesis, the first part aims to study the possibility of using finite element analysis as a tool for predicting shear cracking for plane state stresses. The second part is concerning how the shear cracks are treated in the concrete design standards. Shear cracking in reinforced beams has been studied with non-linear finite element analyses. In these analyses the shear cracking behaviour was compared to experiments conducted to analyse the shear failure behaviour. Finite element analyses were performed with two different FE programs Abaqus and Atena. The material model used in Atena is a smeared crack model based on damage and fracture theory with either fixed or rotated crack direction. The material model used in Abaqus is based on plasticity and damage theory. The fixed crack model in Atena and the model in Abaqus gave good results for all studied beams. For the two studied deep beams with flanges the results from the rotated crack model were almost the same as obtained with the fixed crack model. The rotated crack model in Atena gave though for some beams a rather poor estimation of the behaviour. The calculation of crack widths of shear cracks has been studied for the long-term load case in the serviceability state for the Gröndal and Alvik bridges, with the means available in the design standards. The methods based on the crack direction corresponding to the principal stress and do not include the effect of aggregate interlocking seems to be too conservative. Two of the studied methods included the effect of aggregate interlocking, it was made either by introducing stresses in the crack plane or implicitly by changing the direction of the crack so that it no longer coincide with the direction of principal stress. For calculations based on probable load conditions, these methods gave estimations of the crack widths that were close to the ones observed at the bridges. Continuous measurements of cracks at the Gröndal and the Alvik bridges have also been included. Monitoring revealed that the strengthening work with post-tensioned tendons has, so far, been successful. It also revealed that the crack width variations after strengthening are mainly temperature dependent where the daily temperature variation creates movements ten times greater than those from a passing light-rail vehicle. Monitoring a crack between the top flange and the webs on the Gröndal Bridge showed that the top flange was moving in a longitudinal direction relative to the web until the strengthening was completed. The crack widths in the sections strengthened solely by carbon fibre laminates seem to increase due to long-term effects. / QC 20101119

Motivated by the results concerning the regularity of solutions to the fractional Navier-Stokes system and questions about the influence of noise on the formation of singularities in hydrodynamic models, we have explored these two problems in the context of the fractional 1D Burgers equation. First, we performed highly accurate numerical computations to characterize the dependence of the blow-up time on the the fractional dissipation exponent in the supercritical regime. The problem was solved numerically using a pseudospectral method where integration in time was performed using a hybrid method combining the Crank-Nicolson and a three-step Runge-Kutta techniques. A highlight of this approach is automated resolution refinement. The blow-up time was estimated based on the time evolution of the enstrophy (H1 seminorm) and the width of the analyticity strip. The consistency of the obtained blow-up times was verified in the limiting cases. In the second part of the thesis we considered the fractional Burgers equation in the presence of suitably colored additive noise. This problem was solved using a stochastic Runge-Kutta method where the stochastic effects were approximated using a Monte-Carlo method. Statistic analysis of ensembles of stochastic solutions obtained for different noise magnitudes indicates that as the noise amplitude increases the distribution of blow-up times becomes non-Gaussian. In particular, while for increasing noise levels the mean blow-up time is reduced as compared to the deterministic case, solutions with increased existence time also become more likely. / Thesis / Master of Science (MSc)