Average power losses due to wind turbine wakes are of the order of 10 to 20% of total power output in large offshore wind farms. Accurately quantifying power losses due to wakes is, therefore, an important part of overall wind farm economics. The focus of this research is to compare different types of models from computational fluid dynamics (CFD) to wind farm models in terms of how accurately they represent wake losses when compared with measurements from offshore wind farms. The ultimate objective is to improve modelling of flow for large wind farms in order to optimize wind farm layouts to reduce power losses due to wakes and loads.The research presented is part of the EC-funded UpWind project, which aims to radically improve wind turbine and wind farm models in order to continue to improve the costs of wind energy. Reducing wake losses, or even reduce uncertainties in predicting power losses from wakes, contributes to the overall goal of reduced costs. Here, we assess the state of the art in wake and flow modelling for offshore wind farms, the focus so far has been cases at the Horns Rev wind farm, which indicate that wind farm models require modification to reduce under-prediction of wake losses while CFD models typically over-predict wake losses. Further investigation is underway to determine the causes of these discrepancies.

SUMMARYIn gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C 1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C 1 finite elements and their perceived computational cost. In this context, the lack of three-dimensional C 1 elements is of particular concern. In this paper we present a new C 1 hexahedral element which, to the best of our knowledge, is the first three-dimensional C 1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C 1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good-quality solutions.

We present a second gradient elastoplastic model for strain‐softening materials based entirely on a finite element displacement formulation. The stress increment is related to both the strain increment and its Laplacian. The displacement field is the only field needed to be discretized using a C1 continuity element. The required higher‐order boundary conditions arise naturally from the displacement field. The model is developed to regularize the ill‐posedness caused by strain‐softening material behaviour. The gradient terms in the constitutive equations introduce an extra material parameter with dimensions of length allowing robust modelling of the post‐peak material behaviour leading to localization of deformation. Mesh insensitivity is demonstrated by modelling localization of deformation in biaxial tests. It is shown that both the thickness and inclination of the shear‐band zone are insensitive to the mesh directionality and refinement and agree with the expected theoretical and experimental values. Copyright © 2001 John Wiley & Sons, Ltd.

The paper investigates reproducing the effects of confining pressure on the behaviour of scaled railway ballast in triaxial tests in discrete element models (DEM). Previous DEM work, using a standard Hertzian elastic contact law with an elastic-perfectly plastic tangential slip model, has been unable to replicate the behaviour observed in laboratory tests across a range of confining pressures without altering both the material stiffness and the inter-particle friction. A new contact law modelling damage at the contacts between particles is introduced. Particle contact is via sphericallycapped conical asperities, which reduce in height if overstressed. This introduces plasticity to the behaviour normal to the contact surface. In addition, the inter-particle friction angle is varied as a function of normalized contact normal force. At relatively low normal forces the friction angle must be increased for peak mobilized friction angles to match the laboratory data, an effect that is attributed to interlocking at the scale of surface roughness. Simulation results show close agreement with laboratory data.

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SUMMARYWe present a general finite element discretization of Mindlin's elasticity with microstructure. A total of 12 isoparametric elements are developed and presented, six for plane strain conditions and six for the general case of three-dimensional deformation. All elements interpolate both the displacement and microdeformation fields. The minimum order of integration is determined for each element, and they are all shown to pass the single-element test and the patch test. Numerical results for the benchmark problem of one-dimensional deformation show good convergence to the closed-form solution. The behaviour of all elements is also examined at the limiting case of vanishing relative deformation, where elasticity with microstructure degenerates to gradient elasticity. An appropriate parameter selection that enforces this degeneration in an approximate manner is presented, and numerical results are shown to provide good approximation to the respective displacements and strains of a gradient elastic solid.

Submarine landslides can cause damaging tsunamis, the height of which scales up with the volume of the displaced mass. The largest underwater landslides are far bigger than any landslides on land, and these submarine megaslides tend to occur on open continental slopes with remarkably low gradients of less than 2°. For geohazard assessments it is essential to understand what preconditions and triggers slope failure on such low gradients. Previous work has suggested that generation of high excess pore pressure due to rapid sediment deposition plays a key role in such failures. However, submarine slope failure also occurs where sedimentation rates are low (<0.15 m/kyr), such as off northwest Africa. We use a fully coupled stress and fluid flow finite element model to test whether such low sedimentation rates can generate sufficient excess pore pressures to cause failure of a 2° slope. The sensitivity of overpressure generation and slope stability is assessed with respect to different sedimentation rates and patterns, sediment consolidation properties, and stratigraphic layer configurations. The simulations show that, in general, it is difficult to generate significant excess pore pressure if sediment accumulation is slow and the only pressure source. However, we identify a sediment compression behavior that can lead to submarine landslides in locations worldwide. Our results imply that compressibility is an important factor for the stability of low gradient continental slopes.

Summary The paper describes the development of a technique to simulate triaxial tests on specimens of railway ballast numerically at the particle scale and its validation with reference to physical test data. The ballast particles were modelled using potential particles and the well‐known discrete element method. The shapes of these elemental particles, the particle size distribution and the number of particles (N = 2800) in each numerical triaxial specimen all matched closely to the real ballast material being modelled. Confining pressures were applied to the specimen via a dynamic triangulation of the outer particle centroids. A parametric study was carried out to investigate the effects on the simulation of timestep, strain rate, damping, contact stiffness and inter‐particle friction. Finally, a set of parameters was selected that provided the best fit to experimental triaxial data, with very close agreement of mobilized friction and volumetric strain behaviour. Copyright © 2015 John Wiley & Sons, Ltd.