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Convex Analysisの二,三の進展について

Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

Soil Behaviour and Critical State Soil Mechanics

The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divises (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

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On dense granular flows.

A granular material is a collection of a large number of discrete solid particles. Generally, the interstices between the particles are filled with a fluid such as air or water, and thus, technically, a granular flow is a multiphase process. However, if the particles are closely packed or if they are much denser than the interstitial fluid, the particles alone-and not the fluid or the fluid-particle interactions-will play the greatest role in momentum transport within the material, in which case the interstitial fluid can be ignored in describing the flow behavior. Granular-material fl ows are generally taken to fall into this limiting category and thus may be considered dispersed single-phase rather than multiphase flows. This review addresses the fluidlike behavior of granular solids and, in particular, those flows for which the material is rapidly sheared. I outline what is currently known about rapid granular flows, discuss the various modeling techniques used to describe the motion of the bulk material, and point out many questions that remain to be answered. Depending on the local stress conditions, a granular material may behave as either an elastic solid or a fluid. When a granular material is showing its elastic-solid behavior, it can support the large loads of building foundations or form i nto hills with finite slopes. However, much of the load is supported across frictional bonds between the particles, and, as such, the system's strength is limited to the loads that those bonds can support. When enough of the bonds have been overcome, the system will fail and begin to flow. The initial failure will consist of many-particle blocks moving relative to one another along shear bands that roughly follow stress characteristics through the material. If the motion occurs slowly, particles will stay in contact and interact frictionally with their neighbors over long periods of time. The failure will continue in this

Rapid granular flows

This paper presents the latest comprehensive literature review of AC and DC microgrid (MG) systems in connection with distributed generation (DG) units using renewable energy sources (RESs), energy storage systems (ESS) and loads. A survey on the alternative DG units' configurations in the low voltage AC (LVAC) and DC (LVDC) distribution networks with several applications of microgrid systems in the viewpoint of the current and the future consumer equipments energy market is extensively discussed. Based on the economical, technical and environmental benefits of the renewable energy related DG units, a thorough comparison between the two types of microgrid systems is provided. The paper also investigates the feasibility, control and energy management strategies of the two microgrid systems relying on the most current research works. Finally, the generalized relay tripping currents are derived and the protection strategies in microgrid systems are addressed in detail. From this literature survey, it can be revealed that the AC and DC microgrid systems with multiconverter devices are intrinsically potential for the future energy systems to achieve reliability, efficiency and quality power supply.

AC-microgrids versus DC-microgrids with distributed energy resources: A review

In the analysis of the undrained loading of laterally loaded piles an important quantity is the ultimate lateral resistance at depth to purely horizontal movement. If the soil is modelled as a perfectly plastic cohesive material then the calculation of this quantity reduces to a plane strain problem in plasticity theory, in which the load is calculated on a long cylinder which moves laterally through an infinite medium. An exact calculation of the load on such a cylinder is presented. If this load is non-dimensionalized with respect to the soil strength and the diameter of the pile, it is found that the load factor varies between for a perfectly smooth pile and for a perfectly rough pile. This result is discussed in the context of previous calculations for the lateral load capacity of piles and is compared with approximate calculations using cavity expansion theory and a wedge failure near the soil surface. La resistance laterale limite en profondeur au seul mouvement horizontal represente un parametre im...

The limiting pressure on a circular pile loaded laterally in cohesive soil

The driven monopile is currently the preferred foundation type for most offshore wind farms. While the static capacity of the monopile is important, a safe design must also address issues of accumulated rotation and changes in stiffness after long-term cyclic loading. Design guidance on this issue is limited. To address this, a series of laboratory tests were conducted where a stiff pile in drained sand was subjected to between 8000 and 60 000 cycles of combined moment and horizontal loading. A typical design for an offshore wind turbine monopile was used as a basis for the study, to ensure that pile dimensions and loading ranges were realistic. A complete non-dimensional framework for stiff piles in sand is presented, and applied to interpret the test results. The accumulated rotation was found to be dependent on relative density, and was strongly affected by the characteristics of the applied cyclic load. Particular loading characteristics were found to cause a significant increase in the accumulated ro...

https://www.icevirtuallibrary.com/doi/pdf/10.1680/geot.7.00196

Response of stiff piles in sand to long-term cyclic lateral loading

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.

Application of Thermomechanical Principles to the Modelling of Geotechnical Materials

Lightly overconsolidated natural clays are commonly anisotropic because of their mode of deposition. They exhibit substantial ranges of approximately linear, reversible (elastic) behaviour at stress levels which do not produce yielding of the particle structure of the clay. The Paper examines the five elastic parameters needed to describe transverse isotropy, sometimes called crossanisotropy. Only three parameters can be measured in triaxial tests, and reasonable assumptions, with easily identifiable physical significance, are proposed which permit extrapolation from triaxial to more general stress conditions. Convenient parameters are identified such as the bulk modulus K, shear modulus G, and a cross modulus J which expresses the relationships in a transversely isotropic soil between mean stress and shear strain and between shear stress and volumetric strain. A least squares solution is used to evaluate these parameters from 76mm diameter triaxial tests on Lake Agassiz clay from Winnipeg, Canada. The so...

Anisotropic elasticity of a natural clay

An analysis of the quasi-static expansion of a cylindrical or spherical cavity in an infinite dilatant elastic-plastic soil is presented Closed form solutions for the stress and displacement fields in the soil during the expansion of the cavity are given The soil is modelled as linear elastic-perfectly plastic, using a non-associated Mohr-Coulomb yield criterion An explicit solution for the pressure-expansion relationship is obtained with no restriction on the magnitude of the deformation It is found, in particular, that the radius of the cavity increases indefinitely as the cavity pressure approaches a finite limiting value This limiting pressure can be determined analytically with the help of a single expansion of an infinite series The novelty of the new solution lies in the introduction of dilation to the analysis of large strain expansion Examples of the implications of the new analysis in geotechnical engineering are discussed L'article presente une analyse de l'expansion quasistatique d'une

Guy T. Houlsby

Papers

The limiting pressure on a circular pile loaded laterally in cohesive soil

Response of stiff piles in sand to long-term cyclic lateral loading

Application of Thermomechanical Principles to the Modelling of Geotechnical Materials

Anisotropic elasticity of a natural clay

Finite cavity expansion in dilatant soils: loading analysis