Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

Performance comparisons between greedy and lagrange algorithms in adaptive MIMO MC-CDMA systems

This paper describes two algorithms for adaptive power and bit allocations in a multiple input multiple output multiple-carrier code division multiple access (MIMO MC-CDMA) system. The first is the greedy algorithm, which has already been presented in the literature. The other one, which is proposed by the authors, is based on the use of the Lagrange multiplier method. The performances of the two algorithms are compared via Monte Carlo simulations. At present stage, the simulations are restricted to a single user MIMO MC-CDMA system, which is equivalent to a MIMO OFDM system. It is assumed that the system operates in a frequency selective fading environment. The transmitter has a partial knowledge of the channel whose properties are measured at the receiver. The use of the two algorithms results in similar system performances. The advantage of the Lagrange algorithm is that is much faster than the greedy algorithm. ©2005 IEEE

Independent detectors for expansion and rotation, and for orthogonal components of deformation

It is well known that optic flow - the smooth transformation of the retinal image experienced by a moving observer - contains valuable information about the three-dimensional layout of the environment. From psychophysical and neurophysiological experiments, specialised mechanisms responsive to components of optic flow (sometimes called complex motion) such as expansion and rotation have been inferred. However, it remains unclear (a) whether the visual system has mechanisms for processing the component of deformation and (b) whether there are multiple mechanisms that function independently from each other. Here, we investigate these issues using random-dot patterns and a forced-choice subthreshold summation technique. In experiment 1, we manipulated the size of a test region that was permitted to contain signal and found substantial spatial summation for signal components of translation, expansion, rotation, and deformation embedded in noise. In experiment 2, little or no summation was found for the superposition of orthogonal pairs of complex motion patterns (eg expansion and rotation), consistent with probability summation between pairs of independent detectors. Our results suggest that optic-flow components are detected by mechanisms that are specialised for particular patterns of complex motion.

Deformation of sand in plane strain and oxisymmetric compression

Small scale laboratory experiments, in which the specimen is considered to represent an element of soil in the soil mass, are essential to the evolution of fundamental theories of mechanical behaviour. In this thesis, plane strain and axisymmetric compression tests, performed on a fine sand, are reported and the results are compared with various theoretical predictions. A new apparatus is described in which cuboidal samples can be tested in either axisymmetric compression or plane strain. The plane strain condition is simulated either by rigid side platens, in the conventional manner, or by flexible side platens which also measure the intermediate principal stress. Close control of the initial porosity of the specimens is achieved by a vibratory method of sample preparation. The strength of sand is higher in plane strain than in axisymmetric compression, and the strains required to mobilize peak strength are much smaller. The difference between plane strain and axisymmetric compression behaviour is attributed to the restrictions on particle movement enforced by the plane strain condition; this results in an increase in the frictional component of shear strength. The stress conditions at failure in plane strain, including the intermediate principal stress, are accurately predicted by a theory based on the stress- dilatancy interpretation of Mohr's circles. Detailed observations of rupture modes are presented and measured rupture plane inclinations are predicted by the stress-dilatancy theory. Although good correlation with the stress-dilatancy theory is obtained during virgin loading, in both axisymmetric compression and plane strain, the stress-dilatancy rule is only obeyed during reloading if the specimen has been unloaded to approximate ambient stress conditions. The shape of the stress-strain curves during pre-peak deformation, in both plane strain and axisymmetric compression, is accurately described bv a combined parabolic-hyperbolic specification.

The deformation behaviour of the collapsing and destructured soils of the Sana'a area and their response to field treatment

Previous work has indicated the presence of collapsing and structured soils in the surface layers underlying Sana's, the capital of Yemen Republic. This study set out initially to define and, ultimately, to alleviate the problem by investigating the deformation behaviour of these soils through both field and laboratory programmes. The field programme was carried out in Sana'a while the laboratory work consisted of two parts, an initial phase at Sana's University carried out in parallel with the field programme on natural and treated soils and the major phase at Aston University carried out on natural, destructured and selected treated soils. The initial phase of the laboratory programme included classification, permeability, and single (collapsing) and double oedometer tests while the major phase, at Aston, was extended to also include extensive single and double oedometer tests, Scanning Electron Microscopy and Energy Dispersive Spectrum analysis. The mechanical tests were carried out on natural and destructed samples at both the in situ and soaked moisture conditions. The engineering characteristics of the natural intact, field-treated and laboratory destructured soils are reported, including their collapsing potentials which show them to be weakly bonded with nil to severe collapsing susceptibility. Flooding had no beneficial effect, with limited to moderate improvement being achieved by preloading and roller compaction, while major benefits were achieved from deep compaction. From these results a comparison between the soil response to the different treatments and general field remarks were presented. Laboratory destructuring reduced the stiffness of the soils while their compressibility was increasing. Their collapsing and destructuring mechanisms have been examined by studying the changes in structure accompanying these phenomena. Based on the test results for the intact and the laboratory destructured soils, a simplified framework has been developed to represent the collapsing and deformation behaviour at both the partially saturated and soaked states, and comments are given on its general applicability and limitations. It has been used to evaluate all the locations subjected to field treatment. It provided satisfactory results for the deformation behaviour of the soils destructed by field treatment. Finally attention is drawn to the design considerations together with the recommendations for the selection of potential improvement techniques to be used for foundation construction on the particular soils of the Sana's region.

Deformation microstructures and recrystallization in heavily worked copper

Deformation microstructures in two batches of commercially pure copper (A and B) of allnost similar composition have been studied after rolling reductions from 5% to 95%. X- ray diffraction, optical metallography, scanning electron microscopy in the back-scattered mode, transmission and scanning electron microscopy have been used to examine the deformation microstructure. At low strains (~10 %) the deformation is accommodated by uniform octahedral slip. Microbands that occur as sheet like features usually on the {111} slip planes are formed after 10% reduction. The misorientations between rnicrobonds ond the matrix are usually small (1 - 2° ) and the dislocations within the bands suggest that a single slip system has been operative. The number of microbands increases with strain, they start to cluster and rotate after 60% reduction and, after 90 %, they become almost perfectly aligned with the rolling direction. There were no detectable differences in deformation microstructure between the two materials up to a deformation level of 60% but subsequently, copper B started to develop shear bands which became very profuse by 90% reduction. By contrast, copper A at this stage of deformation developed a smooth laminated structure. This difference in the deformation microstructures has been attributed to traces of unknown impurity in D which inhibit recovery of work hardening. The preferred orientations of both were typical of deformed copper although the presence of shear bands was associated wth a slightly weaker texture. The effects of rolling temperature and grain size on deformation microstructure were also investigated. It was concluded that lowering the rolling temperature or increasing the initial grain size encourages the material to develop shear bands after heavy deformation. Recovery and recrystallization have been studied in both materials during annealing. During recrystallization the growth of new grains showed quite different characteristics in the two cases. Where shear bands were present these acted as nucleation sites and produced a wide spread of recrystallized grain orientations. The resulting annealing textures were very weak. In the absence of shear bands, nucleation occurs by a remarkably long range bulging process which creates the cube orientation and an intensely sharp annealing texture. Cube oriented regions occur in long bands of highly elongated and well recovered cells which contain long range cumulative micorientations. They are transition bands with structural characteristics ideally suited for nucleation of recrystallization. Shear banding inhibits the cube texture both by creating alternative nuclei and by destroying the microstructural features necessary for cube nucleation.