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Parallel, similar and constrained folds 总被引：1，自引：0，他引：1
Theoretical analysis of folding of viscous multilayers with free slip or bonding at layer contacts indicates that folds in such multilayers can be described in terms of three end-members:parallel, in which orthogonal thicknesses of layers are largely constant;similar, in which vertical thicknesses of layers and shapes of successive interfaces are essentially constant; andconstrained, in which amplitudes of anticlines and synclines decrease to zero at upper and lower boundaries. Constrained,internal folds form if the multilayer is confined by rigid media; parallel,concentric-like folds form if the multilayer is confined by soft media, provided soft interbeds are sufficiently thin for the stiff layers to fold as an ensemble. Similar,sinusoidal orchevron folds form throughout much of the thickness of a multilayer, for any stiffness of confining media, provided wavelengths of folds are short relative to the thickness of the multilayer or soft interbeds are sufficiently soft and thick for the stiff layers to act independently. The analysis shows that multilayer folds may have the same form regardless of whether the layer contacts are freely slipping or bonded.
The forms of folds in multilayers confined by media with different viscosities above and below depend on the viscosity contrast of the media. For no medium above and a rigid medium below, the forms are concentric-like in the upper part and internal in the lower part of the multilayer. For no medium above and a soft medium below, the folds are concentric-like throughout the multilayer.
The theory indicates that a useful way to analyze forms of folds in rocks or in experiments is in terms of component waveforms, as defined, for example, by Fourier series. The distributions of amplitudes of component waveforms throughout the multilayer appears to be diagnostic, reflecting contrasts in properties of the multilayer and its confining media. Analysis of a large fold in the central Appalachians, Pennsylvania, and of a smaller fold in the Huasna syncline, California, indicates that at least three component waveforms are required to produce the gross forms of those folds.
The theory closely predicts wavelengths and shapes of folds produced in analogous elastic multilayers, indicating that nonlinearities in material behavior, which are inherent in the elastic material but are absent in the viscous material, are less significant than nonlinearities in the boundary conditions, which are the same in elastic and viscous materials. 相似文献
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Most folds in stratified rock are similar in form to ideal kink, concentric or chevron folds, in which there are discontinuities in slope or curvature of bedding planes. In this respect most folds appear to be closely related to faults, traces of which can be considered to be lines across which there are discontinuities of displacement of layers. Further, the close association of reverse faults and folds or monoclinal flexures seems to indicate that theories of faulting and folding should be closely related.The theory of characteristics is a mathematical tool with which we can obtain insights into processes involving discontinuities. Theoretical characteristic lines are directions across which certain variables might be discontinuous and they are directions along which discontinuities propagate. The theory has been widely applied in plasticity theory and in fluid mechanics and theoretical studies of faulting have suggested that faults are analogous to the lines of discontinuity predicted by plasticity theory. Elasticity and viscosity theories, on which theories of folding have been founded, exclude the existence of characteristic lines in the materials unless the equilibrium equations, rheological properties or strains are nonlinear. However, all folding theories are nonlinear to some extent and the theories can be modified so that they predict lines of discontinuity for some conditions of loading and deformation.Theories of folding will be developed in subsequent papers of this series in order to predict conditions under which characteristic lines can exist in multilayered materials and in order to determine the conditions that must be satisfied across and along the characteristic lines. The theory should help us to recognize lines of apparent discontinuity in natural and experimental folds and study of these lines should provide further understanding of mechanisms of folding.Experimental studies of folding of a wide variety of materials, including alternating layers of rubber and gelatin, modeling clay and grease or graphite, and potter's clay and rubber or cardboard, suggest that the patterns of folding in these materials begin with sinusoidal forms, transform into concentric or kink forms and then into chevron forms as the multilayers are shortened axially. A suitable theory of folding of multilayers should account for these observations. 相似文献
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Misund Ole Arve; Aglen Asgeir; Beltestad Arvid K.; Dalen John 《ICES Journal of Marine Science》1992,49(3):305-315
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The exchange flow of water and sediment between a harbor and the surrounding waters can be geometrically decomposed into three main components: tidal filling, horizontal, and vertical exchange flows. The method is applied to analyze available measurements at two important harbor basins in Belgium. The geometric analysis can also be applied to the results of a numerical model of hydrodynamics and sediment transport, provided it has sufficient horizontal, vertical, and temporal resolutions to capture the dynamics at the harbor mouth. As such, it can be used as a tool in model calibration. The presented method can provide some insight into the complex relationship (phasing and spatial correlations) between hydrodynamics and sediment concentration that determines harbor siltation. 相似文献
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Günther Meinrath Broder Merkel Arvid
degaard‐Jensen Christian Ekberg 《洁净——土壤、空气、水》2004,32(2):154-160
Assessment of the likely outcome of engineered invention strategies in acid mine drainage often involves complex geochemical modelling activities. Geochemical modelling is based on chemical thermodynamic data. In addition sorption models, kinetical reaction rates and transport tools are included into the modelling codes because the interactions between solution components and surfaces, reaction time and transport are considered important features characterising the site‐specific situation. In the determination of both thermodynamic data and sorption coefficients, speciation calculations play an important role. By applying the probabilistic speciation code Ljungskile to some simplified acid mine drainage scenarios, the strong impact of chemical speciation on the complete measurement uncertainty budget of geochemical modelling predictions is shown. The complete measurement uncertainty budget in combination with other metrological concepts like traceability is an essential element of quality assurance for experimental data. The elements of quality assurance are provided by international agreements and normative documents on national and international levels. The following discussion will focus on some metrological issues of sorption data. 相似文献
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The purpose of this paper is to clarify the concept of residual stress in rock. Residual stress is stress near a point in a body subjected to zero external tractions and to zero temperature gradients, excluding body forces. Thus, residual stresses can develop in rock if there are local phase transformations, inelastic strains, or differences in thermal or elastic properties. In these cases, residual stresses can result from changes in temperature, applied stress or configuration of the body.Analysis of residual stresses at the scale of mineral grains within a polycrystalline aggregate such as rock is virtually intractable. One can, however, obtain important insights into residual stresses within bodies with widely spaced sources of residual stress, such as inclusions, and within bodies comprised of multilayers. The analyses indicate that patterns of residual stress in rock can be expected to be extremely complicated. For example, study of residual stresses in a body containing a circular inclusion indicates that:
- 1. (1) There is a single state of residual stress within an inclusion but the state within the surrounding medium is variable. Thus, values of residual stress within rocks reported in the literature generally are of minor value because the sizes and shapes of the sources and the positions of the measurements relative to the positions of sources of residual stresses in the bodies have not been determined.
- 2. (2) Residual stresses within an inclusion can be tensile or compressive, even though the applied stresses were compressive, depending upon the source of residual stress.
- 3. (3) The magnitudes and orientations of residual stresses in an isolated body of rock containing one or more inclusions depends upon the size and shape of the body. The same general conclusions are derived from an analysis of residual stresses in a simple multilayered body.
- 4. (4) In addition, however, the anisotropy of a multilayered body tends to cause principal residual stresses to parallel the layers rather than to parallel the applied stresses that were responsible for inducing the residual stresses. Thus, without identifying the sources of residual stresses in a body, one cannot infer the directions of principal tectonic stresses that might have been responsible for the residual stresses.
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Development of faults as zones of deformation bands and as slip surfaces in sandstone 总被引：10，自引：0，他引：10
Three forms of fault are recognized in Entrada and Navajo Sandstones in the San Rafael Desert, southeastern Utah; deformation bands, zones of deformation bands, and slip surfaces. Small faults occur asdeformation bands, about one millimeter thick, in which pores collapse and sand grains fracture, and along which there are shear displacements on the order of a few millimeters or centimeters. Two or more deformation bands adjacent to each other, which share the same average strike and dip, form azone of deformation bands. A zone becomes thicker by addition of new bands, side by side. Displacement across a zone is the sum of displacements on each individual band. The thickest zones are about 0.5 m and total displacement across a thick zone rarely exceeds 30 cm. Finally,slip surfaces, which are through-going surfaces of discontinuity in displacement, form at either edge of zones of highly concentrated deformation bands. In contrast with individual deformation bands and zones of deformation bands, slip surfaces accommodate large displacements, on the order of several meters in the San Rafael Desert.The sequence of development is from individual deformation bands, to zones, to slip surfaces, and each type of faulting apparently is controlled by somewhat different processes. The formation of zones apparently involves strain hardening, whereas the formation of slip surfaces probably involves strain softening of crushed sandstone. 相似文献