Generalized strain probing of constitutive models

Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate‐independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane‐strain strain probe (PSSP), are used to generate 3‐D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto‐plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd.     

Theoretical accuracy of synthetic aperture sonar micronavigation using a displaced phase-center antenna

The Cramer-Rao lower bounds on the cross-track translation and rotation of a displaced phase-center antenna (DPCA) in the slant range plane between two successive pings (known as DPCA sway and yaw in what follows) are computed, assuming statistically homogeneous backscatter. These bounds are validated using experimental data from a 118-182-kHz sonar, showing an accuracy of the order of 20 microns on the ping-to-ping cross-track displacements. Next, the accuracy required on the DPCA sway and yaw in order to achieve a given synthetic aperture sonar (SAS) beampattern specification, specified by the expected SAS array gain, is computed as a function of the number P of pings in the SAS. Higher accuracy is required when P increases to counter the accumulation of errors during the integration of the elementary ping-to-ping estimates: the standard deviation must decrease as P/sup -1/2/ for the DPCA sway and P/sup -3/2/ for the yaw. Finally, by combining the above results, the lower bounds on DPCA micronavigation accuracy are established. These bounds set an upper limit to the SAS length achievable in practice. The maximum gain Q in cross-range resolution achievable by a DPCA micronavigated SAS is computed as a function of the key SAS parameters. These theoretical predictions are compared with simulations and experimental results.     

Metamorphism in Archaean greenstone belts: calculated fluid compositions and implications for gold mineralization

An inescapable consequence of the metamorphism of greenstone belt sequences is the release of a large volume of metamorphic fluid of low salinity with chemical characteristics controlled by the mineral assemblages involved in the devolatilization reactions. For mafic and ultramafic sequences, the composition of fluids released at upper greenschist to lower amphibolite facies conditions for the necessary relatively hot geotherm corresponds to those inferred for greenstone gold deposits (X_CO2= 0.2–0.3). This result follows from the calculation of mineral equilibria in the model system CaO–MgO–FeO–Al₂O₃–SiO₂–H₂O–CO₂, using a new, expanded, internally consistent dataset. Greenstone metamorphism cannot have involved much crustal over-thickening, because very shallow levels of greenstone belts are preserved. Such orogeny can be accounted for if compressive deformation of the crust is accompanied by thinning of the mantle lithosphere. In this case, the observed metamorphism, which was contemporaneous with deformation, is of the low-P high-T type. For this type of metamorphism, the metamorphic peak should have occurred earlier at deeper levels in the crust; i.e. the piezothermal array should be of the ‘deeper-earlier’type. However, at shallow crustal levels, the piezothermal array is likely to have been of ‘deeper-later’type, as a consequence of erosion. Thus, while the lower crust reached maximum temperatures, and partially melted to produce the observed granites, mid-crustal levels were releasing fluids prograde into shallow crustal levels that were already retrograde. We propose that these fluids are responsible for the gold mineralization. Thus, the contemporaneity of igneous activity and gold mineralization is a natural consequence of the thermal evolution, and does not mean that the mineralization has to be a consequence of igneous processes. Upward migration of metamorphic fluid, via appropriate structurally controlled pathways, will bring the fluid into contact with mineral assemblages that have equilibrated with a fluid with significantly lower X_CO2. These assemblages are therefore grossly out of equilibrium with the fluid. In the case of infiltrated metabasic rocks, intense carbonation and sulphidation is predicted. If, as seems reasonable, gold is mobilized by the fluid generated by devolatilization, then the combination of processes proposed, most of which are an inevitable consequence of the metamorphism, leads to the formation of greenstone gold deposits predominantly from metamorphic fluids.     

Response of circular footings and anchor plates in non-homogeneous elastic soils

The axisymmetric elastic response of circular footings and anchor plates in a linearly non-homogeneous elastic soil is analysed. It is assumed that footings/anchors are flexible and subjected to axisymmetric vertical loads. The response of the footing/anchor is modelled by using the classical Poisson–Kirchhoff thin plate theory. A variational technique is used to analyse the interaction problem. A representation for the contact stress is established by using a fundamental solution corresponding to a unit vertical pressure acting over an annular region in the interior of the non-homogeneous soil. The fundamental solution can be derived by using rigorous analytical procedures. The influence of the footing flexibility and the degree of soil non-homogeneity on the displacements, bending moments and contact stresses of a surface footing is examined over a wide range of governing parameters. In the case of anchor plates the influence of depth of embedment, degree of soil non-homogeneity and anchor flexibility on the anchor displacement is investigated.     

Small angle neutron scattering by opals

Micro- and non-crystalline opals, chalcedony and flint show diffuse small angle neutron scattering (SANS). Precious opals give rise to two additional intensity maxima at very small scattering angles which are due to Bragg reflections from the closest packed non-crystalline silica spheres. A small angle texture diagram reveals that the closest packing is faulty. Synthetic non-crystalline opals yield much less intense small angle scattering due to lower contrast between silica spheres and interstitial cement or particles; in this case intensity maxima were not observed. The outer part of the scattering curves of opal-CT and microcrystalline quartz deviates from Porod's law. The specific surface of natural non-crystalline opals ranges from 0.006 to 0.018 nm^–1. In microcrystalline opals, the specific surface is about 10 times larger than in non-crystalline opals.     

A chum scale pattern analyzer and stock identification based onscale patterns by discriminant function and power spectrum analysis

An optoelectronic instrument has been developed to analyze the scales and scale patterns of chum salmon. This device, with specially developed software, has been used to study populations of salmon. Fish from two different rivers approximately 200 km apart from each other were grouped with an accuracy of 82% or more. Machine-measured ages coincided with those derived from visual estimation in approximately 80% of the fish sampled. These results suggest the proposed system could be of practical use for measuring and analyzing the scale patterns that allow one to accurately measure both natural and farmed populations of salmon     

Comparison of results from several AOGCMs for global and regional sea-level change 1900–2100

 Sea-level rise is an important aspect of climate change because of its impact on society and ecosystems. Here we present an intercomparison of results from ten coupled atmosphere-ocean general circulation models (AOGCMs) for sea-level changes simulated for the twentieth century and projected to occur during the twenty first century in experiments following scenario IS92a for greenhouse gases and sulphate aerosols. The model results suggest that the rate of sea-level rise due to thermal expansion of sea water has increased during the twentieth century, but the small set of tide gauges with long records might not be adequate to detect this acceleration. The rate of sea-level rise due to thermal expansion continues to increase throughout the twenty first century, and the projected total is consequently larger than in the twentieth century; for 1990–2090 it amounts to 0.20–0.37 m. This wide range results from systematic uncertainty in modelling of climate change and of heat uptake by the ocean. The AOGCMs agree that sea-level rise is expected to be geographically non-uniform, with some regions experiencing as much as twice the global average, and others practically zero, but they do not agree about the geographical pattern. The lack of agreement indicates that we cannot currently have confidence in projections of local sea-level changes, and reveals a need for detailed analysis and intercomparison in order to understand and reduce the disagreements. Received: 1 September 2000 / Accepted: 20 April 2001     

Grain boundary diffusion in enstatite

We have investigated grain boundary diffusion rates in enstatite by heating single crystals of quartz packed in powdered San Carlos olivine (Mg_0.90Fe_0.10)₂SiO₄ at controlled oxygen fugacities in the range 10^?5.7 to 10^?8.7?atm and temperatures from 1350° to 1450?°C for times from 5 to 100?h at 1?atm total pressure. Following the experiments, the thickness of the coherent polycrystalline reaction rim of pyroxene that had formed between the quartz and olivine was measured using backscatter scanning imaging in the electron microprobe. Quantitative microprobe analysis indicated that the composition of this reaction phase is (Mg_0.92Fe_0.08)₂Si₂O₆. The rate of growth of the pyroxene increases with increasing temperature, is independent of the oxygen fugacity, and is consistent with a parabolic rate law, indicating that the growth rate is controlled by ionic diffusion through the pyroxene rim. Microstructural observations and platinum marker experiments suggest that the reaction phase is formed at the olivine-pyroxene interface, and is therefore controlled by the diffusion of silicon and oxygen. The parabolic rate constants determined from the experiments were analyzed in terms of the oxide activity gradient across the rim to yield mean effective diffusivities for the rate-limiting ionic species, assuming bulk transport through the pyroxene layer. These effective diffusivities are faster than the lattice diffusivities for the slowest species (silicon) calculated from creep experiments, but slower than measured lattice diffusivities for oxygen in enstatite. Thus, silicon grain boundary diffusion is most likely to be the rate-limiting process in the growth of the pyroxene rims. Also, as oxygen transport through the pyroxene rims must be faster than silicon transport, diffusion of oxygen along the grain boundaries must be faster than through the lattice. The grain boundary diffusivity for silicon in orthopyroxenite is then given by D¯gbSiδ=(3.3±3.0)×10^?9f0.0O₂e^?400±65/RT?m³s^?1, where the activation energy for diffusion is in kJ/mol, and δ is the grain boundary width in m. Calculated growth rates for enstatite under these conditions are significantly slower than predicted by an extrapolation from similar experiments performed at 1000?°C under high pressure (hydrous) conditions by Yund and Tullis (1992), perhaps due to water-enhancement of diffusion in their experiments.     

Occurrence of noble metals in aluminum- and chromium- rich objects in ordinary chondrites and of baddeleyite (ZrO2) in a chromite inclusion

Abstract— Platinum group elements (PGE) enrichments are found in Fe-Ni blebs (<1 μm) in Al- and Cr-rich objects in the ordinary chondrites Ste. Marguerite, Forest Vale, Montferré. In Ste. Marguerite, high ZrO₂ concentrations (baddeleyite) are also present in a chromite inclusion. Iridium enrichment in this material compared to its metal content is confirmed by INAA. The widespread occurrence of PGE in Al- and Cr-rich objects, mostly present in H-group chondrites of nearly equilibrated types, must be taken into account to understand their conditions of formation.