G. T. Houlsby

APPLICATION OF THERMOMECHANICAL PRINCIPLES TO THE MODELLING OF GEOTECHNICAL MATERIALS

A thermodynamic framework is presented for the plasticity modelling of geotechnical materials. The framework is capable of modelling rigorously both friction and non-associated flow, and the strong connection between these phenomena is demonstrated. The formulation concentrates on the development of constitutive models from hypotheses about the form of an energy potential and a dissipation function. The reformulation of previous work, in which the Helmholtz free energy was used, to a new approach starting from the Gibbs free energy is found to be valuable. The relationship between the new functions and classical plasticity concepts (yield surface, plastic potential, isotropic and kinematic hardening, friction, dilation) is demonstrated. Comments are made on elastic-plastic coupling. Implications of the new approach for critical state soil models are discussed.

A thermomechanical framework for constitutive models for rate-independent dissipative materials

Abstract A formulation of elastic–plastic theory for rate independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depending on which combinations of the stress, strain, temperature and entropy are taken as the independent variables. Much use is made of Legendre transformations to establish the links between the different energy functions. Dissipative behaviour is introduced through the use of kinematic internal parameters, and their conjugate variables, which are termed generalised stresses. A dissipation function or a yield function is used to describe the irreversible behaviour, and these are related by a degenerate case of the Legendre transformation. A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. A systematic presentation is made of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of the two potentials and by standard matrix manipulation. Examples are provided of the forms of the potentials for certain simple cases. The paper builds on previous work by Ziegler and other authors, and extends and generalises work by Collins and Houlsby to include thermal effects.

Foundations for offshore wind turbines.

An important engineering challenge of today, and a vital one for the future, is to develop and harvest alternative sources of energy. This is a firm priority in the UK, with the government setting a target of 10% of electricity from renewable sources by 2010. A component central to this commitment will be to harvest electrical power from the vast energy reserves offshore, through wind turbines or current or wave power generators. The most mature of these technologies is that of wind, as much technology transfer can be gained from onshore experience. Onshore wind farms, although supplying ‘green energy’, tend to provoke some objections on aesthetic grounds. These objections can be countered by locating the turbines offshore, where it will also be possible to install larger capacity turbines, thus maximizing the potential of each wind farm location. This paper explores some civil–engineering problems encountered for offshore wind turbines. A critical component is the connection of the structure to the ground, and in particular how the load applied to the structure is transferred safely to the surrounding soil. We review previous work on the design of offshore foundations, and then present some simple design calculations for sizing foundations and structures appropriate to the wind-turbine problem. We examine the deficiencies in the current design approaches, and the research currently under way to overcome these deficiencies. Designs must be improved so that these alternative energy sources can compete economically with traditional energy suppliers.

THE USE OF A VARIABLE SHEAR MODULUS IN ELASTIC-PLASTIC MODELS FOR CLAYS

Abstract When modelling the elastic behaviour of a clay it is often convenient to use a shear modulus which is proportional to the mean effective stress, in order to improve the accuracy of modelling. This choice can lead, however, to theoretical difficulties, in that the elastic behaviour may be non-conservative. These difficulties may be reflected as inaccuracies in calculations, particularly if cyclic loading is involved. A framework within which a pressure dependent shear modulus can be accomodated in a theoretically acceptable manner is described. Some experimental evidence for the variation of shear modulus with pressure is also discussed.

Suction Caisson Foundations for Offshore Wind Turbines and Anemometer Masts

We describe briefly some of the challenges met by the designers of the foundation systems for offshore wind energy developments. Although some experience from the offshore oil and gas industry proves valuable, the size and nature of typical wind turbines means that the loadings on the foundations are quite different from those encountered previously offshore. The most economical solutions are also likely to differ from those conventionally used offshore. We highlight the possibilities of a novel form of foundation: the suction caisson.

Suction Caisson Foundations for Offshore Wind Turbines

This paper outlines a £ 1.5m, three year, research project that commenced during the middle of 2002 to determine a design framework for shallow foundations for offshore wind turbines. The shallow foundations in focus are suction-installed skirted foundations otherwise known as suction caissons (Houlsby and Byrne, 2000). There are eight distinct themes to the research covering all aspects of the geotechnical performance of these foundations. The funding for the project has been obtained from the Department of Trade and Industry (£ 917k), Industrial Partners (£ 373k) and the Engineering and Physical Sciences Research Council (£ 221k). The results will feed into the design process for offshore wind turbines almost immediately.

The available power from tidal stream turbines in the Pentland Firth

This paper assesses an upper bound for the tidal stream power resource of the Pentland Firth. A depth-averaged numerical model of the tidal dynamics in the region is set-up and validated against field measurements. Actuator disc theory is used to model the effect of turbines on the flow, and to estimate the power available for generation after accounting for losses owing to mixing downstream of the turbines. It is found that three rows of turbines extending across the entire width of the Pentland Firth and blocking a large fraction of the channel can theoretically generate 1.9 GW, averaged over the spring–neap cycle. However, generation of significantly more power than this is unlikely to be feasible as the available power per additional swept area of turbine is too small to be viable. Our results differ from those obtained using simplified tidal channel models of the type used commonly in the literature. We also use our numerical model to investigate the available power from rows of turbines placed across various subchannels within the Pentland Firth, together with practical considerations such as the variation in power over the spring–neap tidal cycle and the changes to natural tidal flows which result from power extraction.

An implementation of Watson's algorithm for computing 2-dimensional Delaunay triangulations

Abstract A FORTRAN 77 implementation of Watsons algorithm for computing two-dimensional Delaunay triangulations is described. The algorithm is shown to have an asymptotic time complexity bound which is better than O(N 1.5 ) by applying it to collections of N points generated randomly within the unit square. The computer code obeys strict FORTRAN 77 syntax. Excluding the memory needed to store the co-ordinates of the points, it requires slightly greater than 9N integer words of memory to assemble and store the Delaunay triangulation.

Long-Term Lateral Cyclic Response of Suction Caisson Foundations in Sand

AbstractSkirted gravity base foundations and suction caisson foundations are considered as viable alternatives to monopile foundations for offshore wind turbines. While recent work has focused on the monotonic moment-rotation response for shallow foundations, the cyclic response and the accumulation of rotation over the life of the turbine must also be addressed. This paper presents cyclic loading tests where approximately 10,000 cycles, with different loading characteristics, were applied to a model shallow foundation (a caisson) in loose sand. On the basis of these tests, a framework for assessing the accumulated angular rotation because of cycling was developed. The settlement and cyclic stiffness response of the caisson were also assessed. It was found, not unexpectedly, that the accumulated settlement of the caisson increased with the number of cycles and cyclic amplitude. It was also found that a cyclic loading regime intermediate between one-way and full two-way cycling produced the largest rotatio...

A thermomechanical framework for rate-independent dissipative materials with internal functions

Abstract This paper builds on previous work by Houlsby and Puzrin (Int. J. Plasticity 16 (2000) 1017) in which a framework was set out for the derivation of rate-independent plasticity theory from thermodynamic considerations. A key feature of the formalism is that the entire constitutive response is determined by knowledge of two scalar functions. The loading history is effectively captured through the use of internal variables. In this paper, we extend the concept of internal variables to that of internal functions, which represent infinite numbers of internal variables. In this case the thermodynamic functions are replaced by functionals. We set out the formalism necessary to derive constitutive behaviour within this approach. The principal advantages of this development is that it can provide realistic modelling of kinematic hardening effects and smooth transitions between elastic and elastic–plastic behaviour.