Ac Palmer

Fractal Crushing of Ice and Brittle Solids

A significant ‘scale effect’ is observed when sea ice forces on structures are measured at field scale: the force per unit contact area is not independent of area, but decreases with increasing area. Fragments of broken materials are found to have a fractal size distribution, with a fractal dimension close to 2.5 over a remarkably wide range of fragment size. The research described in this paper brings these two observations together, and shows that they can be explained by a simple model of crushing, which incorporates the relation between fragment size and splitting force predicted by linear elastic fracture mechanics. The model indicates a special role for the fractal dimension of 2.5, and predicts a relation between force and area, consistent with field observations.

NORMALITY RELATIONS AND CONVEXITY OF YIELD SURFACES FOR UNSTABLE MATERIALS OR STRUCTURAL ELEMENTS.

Abstract : The stress-strain relations for materials and the load-deflection relations for structural elements play corresponding roles in the analysis of three-dimensional continua and of structures respectively. Mathematically equivalent and phenomenologically quite similar, they are treated simultaneously here. As in previous treatments of stable (rising) plastic stress-strain curves, unstable (falling) curves in simple shear or tension are generalized to all states of stress through the exploration of the work done in a cycle of stress (Drucker) and in a cycle of strain (Ilyushin). The plastic increment of strain is found to be normal to the current yield surface for a wide class of unstable materials in which a continuous variation of strain produces a unique continuous variation of stress and of the shape and position of the yield surface. In the absence of any significant alteration in the (stable) elastic response, each yield surface then is shown to be convex. The degree of concavity possible when the elastic response is stable but is non-linear and does alter appreciably due to plastic deformation is illustrated by a non-linear elastic spring and a plastic block in parallel. Such concavity would not be observable in the yield surfaces of common structural metals, but might be found for soils, rocks or concrete and can be quite pronounced for structural elements. (Author)

Experimental study of marine pipelines on unstable and liquefied seabed

Experimental investigation was carried out in a wave flume to study the stability of marine pipelines on mobile and liquefied seabed. A wide range of different pipeline specific gravities and wave condition were examined. The results showed that for the given soil the seabed response is governed mainly by liquefaction and the pipeline behaviour on unstable seabed is strongly dependent on its specific gravity.

DESIGN OF SUBMARINE PIPELINES AGAINST UPHEAVAL BUCKLING

The paper describes part of a comprehensive joint-industry project on upheaval buckling. It develops a semi-empirical simplified design method and detailed design methods based on a new numerical analysis, and illustrates their application by examples. It assesses alternative design strategies, and the implications of strain-based design.

Fracture and its role in determining ice forces on offshore structures

One of the most conspicuous phenomena in the Arctic is the fracture of sea ice. It is scarcely possible to travel far without seeing a variety of fracture forms, produced both by natural processes and by human activity. At strain-rates below about 10-4 s-l, deformation is dominated by creep, but at higher strainrates fracture is much more important. One of the reasons for this is the very low fracture toughness of ice. The movements of ice in contact with offshore structures often induce strain-rates well beyond the level at which fracture begins, and so offshore structures will often operate in the fracture regime, and it is fracture processes which will determine the design loads. We consider the different modes of repeated fracture that will occur, and classify them into distinct mechanisms of crushing, spalling, and radial and circumferential cracking. Experimental and field observations are plotted on a deformation mode map. A theoretical treatment of radial cracking confirms that very low loads can propagate cracks to long distances; these loads are small by comparison with those calculated from theoretical models that treat ice as a plastically-deforming continuum.

The force exerted by a moving ice sheet on an offshore structure: Part 1. The creep mode

Abstract A uniform ice sheet moves steadily against a flat-sided fixed offshore structure. The ice deforms in creep: the problem is to determine the relation between the force on the structure and the velocity of the ice. The problem cannot be solved analytically, but a conventient approximate solution can be found by the reference stress method of creep structural analysis, which makes systematic use of a small number of numerical and analytic solutions to related problems, including solutions to the corresponding problem for a perfectly-plastic material. The method is applicable to any observed relation between stress and strain rate. It is tested by comparison with additional numerical solutions, and with published data on indentation experiments.

High pressure zone formation during compressive ice failure

Abstract An understanding of the mechanics and physics of the formation of the high pressure zones that form during ice–structure interactions is sought. The influences of time, temperature and scale on the formation of these high pressure zones are explored in this paper. Line-like and localized high pressure contact zones are modeled via elastic-brittle hollow cylinder and hollow sphere idealizations, respectively. For both simultaneous and non-simultaneous contact, the critical lengths of stable cracking that may occur prior to flaking and flexural failure are strongly linked to the current level of specific pressure parameters for both line-like and localized high pressure zones. The stability aspects of the in-plane cracking, and the link between the maximum possible crack lengths and the relative magnitudes of the local and far-field pressures help explain the transitions observed within the realms of ductile, intermittent, and brittle crushing.

Optimal design of transmission towers by dynamic programming

Abstract Dynamic programming has been found a useful technique for the synthesis of optimal layouts for braced frameworks, provided that the interconnection between different parts of the structure is relatively simple. Its application to real structures has been explored by a study of the optimal design of the steel towers used to carry overhead lines. Many practical features complicate the problem, and make it inaccessible to classical techniques such as the theory of Michell structures. There are strong geometric constraints on layout, and yet many topologically distinct possible configurations, there are several alternative loadings to be taken into account, and in addition the design of many of the bars is constrained by buckling rather than by a fixed allowable stress level. It has proved possible to include these and similar factors in a computer program which uses dynamic programming to synthesise optimal designs. The program generates designs significantly lower in weight than existing designs.

Lateral Resistance Of Marine Pipelines On Sand

Within a wider research investigation of lateral stability of marine pipelines, a geotechnical investigation was carried out to examine lateral resistance to movement. It included extensive full-scale tests on a nominal 10 inch pipe on sand, under a range of loading conditions designed to simulate the loading history of a pipeline on the seabed. The results showed that the lateral resistance is actually higher than is generally assumed. The effect is particularly marked when the loading is cyclic with increasing amplitude, and when the pipe is partially embedded in the seabed.

Ice lensing, thermal diffusion and water migration in freezing soil

WHEN A SURFACE LAYER OF THE SOIL FREEZES, BOTH HEAT AND WATER DIFFUSED FROM THE UNFROZEN SOIL BENEATH TO THE FROZEN REGION. OFTEN THE SOIL DOES NOT FREEZE HOMOGENEOUSLY BUT DISTINCT ICE LENSES FORM. AN ANALYSIS OF THE DIFFUSION AND ICE NUCLEATION PROCESSES SUGGESTS CONDITIONS UNDER WHICH ICE LENSING CAN BE EXPECTED; IN PARTICULAR, IT IS SHOWN THAT MULTIPLE ICE LENSES CANNOT FORM UNLESS THE SOIL THERMAL DIFFUSIVITY IS GREATER THAT THE WATER DIFFUSION COEFFICIENT. ANALYSIS OF A SIMPLE ONE-DIMENSIONAL CASE (A SEMI-INFINITE MASS OF HOMOGENEOUS SOIL WHOSE SURFACE TEMPERATURE IS SUDDENLY LOWERED) GIVES THE TEMPERATURE AND WATER-CONTENT FIELDS AS FUNCTIONS OF TIME; THESE AGREE WITH THOSE OBSERVED IN A EXPERIMENTAL STUDY OF FREEZING CLAY. /RRL/A/