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1.
Six experiments of single-layer folding with simple-shear boundary conditions were completed. Using materials of ethyl cellulose, the viscosity ratio of the stiff layer to matrix ranged from 20 to 100. The experiments were monitored by 10–14 photographs taken at equally spaced time intervals. Strain distributions in both the stiff layer and matrix were calculated from the displacements of over 300 ink dots distributed over the surface of each experiment. Both incremental strain (calculated from the relative displacements of the dots between successive photographs) and accumulating strain were determined on the two-dimensional profile of the materials as they folded.Symmetrical fold wavelengths occur and seem to be controlled by the wavelengths of initial perturbations in the stiff layer. If the Biot wavelength was not present initially, it will not occur in the final waveform. Consequently, in a group of natural folds, the mean value of wavelength/thickness ratios apparently reflects the initial perturbations. The mean value should not be confused with the Biot wavelength and should not be used to calculate viscosity ratios in naturally deformed rocks.Substantial layer thickening occurred only with viscosity ratios of 20. The amount of layer thickening also depends on initial perturbations of the stiff layer. If these perturbations are near the Biot wavelength, they are greatly amplified, the folds grow rapidly and layer thickening is small. If the perturbations are not near the Biot wavelength, amplification is small, the folds grow slowly and layer thickening is much greater.Principal elongations of the accumulated strain in the cores of some of the folds are not symmetrically distributed about axial planes and may cut across the axial plane at angles up to 20°. Strain shadows in the matrix, near the convex side of fold hinges, are also prominent. These triangular-shaped regions of low strain are not symmetrically disposed about fold axial planes, in contrast to strain shadows occurring in folds produced under pure-shear boundary conditions.The rotation of accumulating principal elongations in the stiff layer was calculated at fold inflections. Even though the folds themselves are generally symmetrical, these rotations at opposite fold inflections are not. One fold limb exhibits little rotation of principal elongations during folding while the other has rotations up to 70°. In contrast, folds formed in pure-shear boundary conditions have rotations of principal directions on opposite fold limbs equal in magnitude.  相似文献   

2.
This part concerns folding of elastic multilayers subjected to principal initial stresses parallel or normal to layering and to confinement by stiff or rigid boundaries. Both sinusoidal and reverse-kink folds can be produced in multilayers subjected to these conditions, depending primarily upon the conditions of contacts between layers. The initial fold pattern is always sinusoidal under these ideal conditions, but subsequent growth of the initial folds can change the pattern. For example, if contacts between layers cannot resist shear stress or if soft elastic interbeds provide uniform resistance to shear between stiff layers, sinusoidal folds of the Biot wavelength grow most rapidly with increased shortening. Further, the Biot waves become unstable as the folds grow and are transformed into concentric-like folds and finally into chevron folds. Comparison of results of the elementary and the linearized theories of elastic folding indicates that the elementary theory can accurately predict the Biot wavelength if the multilayers contain at least ten layers and if either the soft interbeds are at most about one-fifth as stiff as the stiff layers, or there is zero contact shear strength between layers.Multilayers subjected to the same conditions of loading and confinement as discussed above, can develop kink folds also. The kink fold can be explained in terms of a theory based on three assumptions: each stiff layer folds into the same form; kinking is a buckling phenomenon, and shear stress is required to overcome contact shear strength between layers and to produce slippage locally. The theory indicates that kink forms will tend to develop in multilayers with low but finite contact shear strength relative to the average shear modulus of the multilayer. Also, the larger the initial slopes and number of layers with contact shear strength, the more is the tendency for kink folds rather than sinusoidal folds to develop. The theoretical displacement form of a layer in a kink band is the superposition of a full sine wave, with a wavelength equal to the width of the kink band, and of a linear displacement profile. The resultant form resembles a one-half sine curve but it is significantly different from this curve. The width of the kink band may be greater or less than the Biot wavelength of sinusoidal folding in the multilayer, depending upon the magnitude of the contact shear strength relative to the average shear modulus. For example, in multilayers of homogeneous layers with contact strength, the Biot wavelength is zero so that the width of the kink band in such materials is always greater than the Biot wavelength. In general, the higher the contact strength, the narrower the kink band; for simple frictional contacts, the widths of kink bands decrease with increasing confinement normal to layers. Widths of kink bands theoretically depend upon a host of parameters — initial amplitude of Biot waves, number of layers, shear strength of contacts between layers, and thickness and modulus ratios of stiff-to-soft layers — therefore, widths of kink bands probably cannot be used readily to estimate properties of rocks containing kink bands. All these theoretical predictions are consistent with observations of natural and experimental kink folds of the reverse variety.Chevron folding and kink folding can be distinctly different phenomena according to the theory. Chevron folds typically form at cores of concentric-like folds; they rarely form at intersections of kink bands. In either case, they are similar folds that develop at a late stage in the folding process. Kink folds are more nearly akin to concentric-like folds than to chevron folds because kink folds form early, commonly before the sinusoidal folds are visible. Whereas concentric-like folds develop in response to higher-order effects near boundaries of a multilayer, kink folds typically initiate in response to higher-order shear, as at inflection points near mid-depth in low-amplitude, sinusoidal fold patterns. Chevron folding and kink folding are similar in elastic multilayers in that elastic “yielding” at hinges can produce rather sharp, angular forms.  相似文献   

3.
Fold shapes and strain distributions produced in stiff single layers inclined up to 20° to the direction of principal shortening were investigated using finite-element computer models. The finite-element model was formulated for constant-strain quadrilaterals using the constitutive equation for a compressible, linearly viscous fluid. The model of a stiff layer imbedded in a less viscous medium was designed to accommodate 2 Biot wavelengths. Inclinations of the stiff layer to the shortening direction were 0°, 5°, 10°, 15° and 20°. At each inclination folds were produced with viscosity ratios of 17 : 1, 24 : 1 and 42 : 1. Folds were initiated by prescribing symmetric sinusoidal perturbations with limb dips of 2°. Results from models with 0° initial inclinations are similar to results obtained by others. Folds are sinusoidal and symmetric, and strain distributions are symmetrically disposed about axial planes in both the matrix and stiff layer. As layer inclination is increased, these features change. The folds become asymmetric (as measured by the ratio of limb lengths), and the amount of asymmetry increases with inclination. Finite-strain distributions in both the stiff layer and matrix are not symmetrically disposed about the axial plane. Principal strains in the matrix tend to parallel the long limb of the stiff layer, and are “refracted” through the long limb at a larger angle than through the short limb.  相似文献   

4.
Twiss (1976) has suggested that the “ductile faulting” events observed by Post (1973) during high temperature creep of dunite are due to a transition from creep by dislocation movement to a diffusion accommodated, grain-boundary sliding mechanism following a reduction in grain size by dynamic recrystallization. Similarly, Goetze (1978) has explained both ductile faulting and water weakening of dunite by transition to a “nonlinear Coble” creep mechanism. However, the fundamental assumption made by Twiss (1976) that the stress exponent, n, reduces to unity during ductile faulting events is questionable. If the stress exponent remains high, (n≥3), then a diffusion-accomodated grain-boundary sliding mechanism is excluded. “Nonlinear Coble” creep would remain a viable alternative; however, this model fails to adequately explain the water weakening phenomenon, and the available data do not constrain us to this model. Assuming that the water-weakening phenomenon can be explained by other models (e.g., Blacic, 1972), it will be shown (by analogy with the behavior of metals) that a third model, also consistent with the available data, also qualitatively explains the observations associated with ductile faulting without appeal to a transition in creep mechanisms. The model is similar to one for metals undergoing deformation by dislocation movement and recovery by dynamic recrystallization, which commonly exhibit behavior virtually identical to that observed in dunite during ductile faulting events without transition to grain-size-sensitive creep mechanisms.  相似文献   

5.
The progressive development of folds by buckling in single isolated viscous layers compressed parallel to the layering and embedded in a less viscous host is examined in several ways; by use of experiments, an analogue model to simulate simultaneous buckling and flattening and by an application of finite-element analysis.The appearance of folds with a characteristic wavelength in an initially flat layer occurs in the experiments for viscosity ratios (μlayerhost = μ12) of between 11 and 100; progressive fold development after the initial folds have appeared is similar in the experiments and in the finite-element models. Except for the finite-element model for μ12 = 1,000 layer-parallel shortening occurs in the early stages of folding and a stage is reached where little further changes in arc length occur. The amount of layer-parallel shortening increases with decreasing viscosity contrast, and becomes relatively unimportant after the folds have attained limb dips of about 15°–25°.Thickness variations with dip are only significant here for the finite-element model with μ12 = 10, and in experiments for μ12 = 5 where the layer is initially in the form of a moderate-amplitude sine wave. The variations range from a parallel to a near-similar fold geometry, and in general depend on the viscosity contrast, the degree of shortening and the initial wavelength/thickness ratio. They are very similar to the variations predicted by the analogue model of combined buckling and flattening. The difference between the thickness/dip variations in a fold produced by buckling at low viscosity contrast and one produced by flattening a parallel fold is marked at high limb dips and very slight at low limb dips.Many natural folds in isolated rock layers or veins show thickness/dip relationships expected for a flattened parallel fold, and some show relationships expected for buckling at low viscosity contrasts. Studies of the wavelength/thickness ratios in natural folds have suggested that competence contrast is often low. Many folds in isolated rock layers or veins whose geometry may vary between parallel and almost similar, and may be indistinguishable from those of flattened parallel folds, have probably developed by a process of buckling at low viscosity contrasts.  相似文献   

6.
The complexity of determining strain associated with shear modulus and damping ratio in torsional tests has been resolved by means of several approaches. The stress integration approach is adequate when generating the plots of equivalent radius ratio versus strain more effectively over any range of strains in resonant column and torsional shear (RC/TS) tests. The stress integration approach was applied for hyperbolic, modified hyperbolic, and Ramberg–Osgood models in evaluating damping ratio. This study showed that using a single value of equivalent radius ratio in evaluating damping ratio is not appropriate. The combined hysteretic‐nonviscous damping model was developed and employed to consider the increased damping behavior at small strains using the stress integration approach. The results suggest that adding viscous behavior has no significant effect strain calculations in RC/TS testing. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

7.
We analyzed and compared the mixing properties of 2-D mantle convection models. Two rheologically different models, Newtonian and non-Newtonian (power-law), were considered with both the line and field methods. The line method is based on monitoring of passive particles joined into lines, while the field method relies on the advection of a passive scalar field. Both visual and quantitative estimates revealed that the efficiency of the Newtonian mixing is greater than the non-Newtonian. A heterogeneity placed in the non-Newtonian convection forms horizontal structures, which may persist for at least 1 Ga on the upper-mantle scale. In addition, the non-Newtonian medium reveals a lesser amount of stretching of the lines than the Newtonian material. The rate of the Newtonian stretching fits well with an exponential dependence with time, while the non-Newtonian rheology shows the stretching rate close to a power-law dependence with time. In the Newtonian medium the heterogeneity is reorganized into two unstable vertical columns, while the non-Newtonian mixing favors horizontal structures. In the latter case, these structures are sufficiently stable in both the temporal and spatial planes to explain the mantle geochemical and geophysical heterogeneities. Due to the non-linear character of power-law rheology, the non-Newtonian medium offers a “natural” scale-dependent resistance to deformation, which prevents efficient mixing at the intermediate length scales.  相似文献   

8.
A new method to estimate strain and competence contrast from natural fold shapes is developed and verified by analogue and numerical experiments. Strain is estimated relative to the nucleation amplitude, AN, which is the fold amplitude when the amplification velocities caused by kinematic layer thickening and dynamic folding are identical. AN is defined as the initial amplitude corresponding to zero strain because folding at amplitudes smaller than AN is dominantly by kinematic layer thickening. For amplitudes larger than AN, estimates of strain and competence contrast are contoured in thickness-to-wavelength (H/λ) and amplitude-to-wavelength (A/λ) space. These quantities can be measured for any observed fold shape. Contour maps are constructed using existing linear theories of folding, a new nonlinear theory of folding and numerical simulations, all for single-layer folding. The method represents a significant improvement to the arc length method. The strain estimation method is applied to folds in viscous (Newtonian), power-law (non-Newtonian) and viscoelastic layers. Also, strain partitioning in fold trains is investigated. Strain partitioning refers to the difference in strain accommodated by individual folds in the fold train and by the whole fold train. Fold trains within layers exhibiting viscous and viscoelastic rheology show different characteristic strain partitioning patterns. Strain partitioning patterns of natural fold trains can be used to assess the rheological behaviour during fold initiation.  相似文献   

9.
孙凯  陈正林  陈剑  徐学燕 《岩土力学》2015,36(Z1):142-146
冻土在高应力水平下通常会表现出加速蠕变特性。经典西原(Nishihara)模型可以反映衰减蠕变和稳态蠕变,但不适用于描述加速蠕变。通过对Nishihara模型中黏性元件进行修正,将黏弹性元件中的定常的黏滞系数修正为时间的函数,并在黏塑性元件中采用非定常、非牛顿黏性元件,得到的蠕变柔量可以考虑应力水平和时间的影响,使其能够反映其加速蠕变的过程。用提出的模型分别对一维和三维应力、不同应力水平下的冻土蠕变试验数据进行了拟合,拟合结果能够反映冻土从衰减蠕变和稳定蠕变状态进入加速蠕变的过程,说明了该模型对于描述冻土在不同应力下不同蠕变状态的适用性。  相似文献   

10.
The presented equation describes amplitude growth during viscous single-layer folding (buckling) up to high amplitudes. The equation relates the dimensionless fold amplitude (i.e. ratio of amplitude to wavelength) to the stretch (ratio of initial wavelength to instantaneous wavelength) for given values of the viscosity contrast between layer and surrounding material and the initial ratio of amplitude to wavelength. The amplification equation is suitably scaled so that all amplitude versus stretch curves for different values of viscosity contrasts and initial amplitudes fall onto essentially a single curve. The scaled amplification equation allows for representing fold amplification of viscous single-layers by a singular curve. The scaling parameter is the crossover strain, which is an estimate for the amount of strain that is accumulated during the initial stages of folding where the amplitude grows exponentially with strain. The singular curve allows quantifying the universal boundaries between the three folding stages, namely nucleation, amplification and kinematic growth. The scaled amplification equation is verified by numerical (finite element method) simulations of folding of single layers with initial random perturbations of the layer interfaces. The amplification equation describes the amplification of single folds within fold trains successfully, although the folds are neither regular nor periodic and vary considerably in shape. The easily measurable parameters, vertical and horizontal hinge distance, are shown to be good approximations for the analytical parameters amplitude and wavelength, respectively.  相似文献   

11.
The offsets on the ocean floor, usually called “transform-faults” are not shear faults common in solid Hookian rocks, but reflect the viscous Newtonian properties of laminar flow at the time when the upwelling magma along the spreading center was still in a liquid state. During spreading this liquid is carried away with the walls of the spreading center. This movement creates a pattern of stream lines in the liquid which run parallel to the direction of spreading. “Transform faults” are initiated along zones where a larger rate of shear disturbs the process of solidification. Consequently the strength of the basalt after solidification will be impaired along these zones. These weak zones will fracture under the thermo-elastic stresses during the final stage of cooling.The history of the term “transform fault” is discussed and the name “spreading offset” is proposed.  相似文献   

12.
The Keystone-Muddy Mountain thrust sheet was displaced for several tens of kilometres across the land's surface in Cretaceous times. Its movement is related to the emplacement of the Sierra Nevada batholith, which provided a source of compressive stress over a period of about 140 Ma.The mechanical analysis presented here examines the stresses operating throughout the whole thrust sheet (i.e. the “toe”, “ramp” and “main thrust block”) which extends for approximately 200 km from front to rear. Frictional sliding can explain only the motion of the toe, the ramp and perhaps part of the main thrust block. A composite model, involving elastic upper and viscous lower layers, is used to account for the movement of most of the main thrust block.  相似文献   

13.
In some metamorphic terrains, lineations in folded surfaces are coaxial to the folds at their hinges, but show a systematic dispersion on the limbs. A simple theoretical model is presented, based on two assumptions: (1) the layering is folded according to two idealised models, “ideal compression folding” and “ideal shear folding”, which assume that the rock material is homogeneous and the layering passive; (2) the lineation is a manifestation of the total product of the pre-folding and folding strains. In an ideal compression fold, only apparent lineations can be dispersed away from the fold-axial trend; in an ideal shear fold, however, both real and apparent lineations are dispersed in a similar way, the degree of similarity depending on the X/Y ratio of the pre-fold strain. The lineation loci of the two models are sufficiently distinct for them to be used, together with other features of the fabric, to distinguish between folds produced by dominantly vertical movements, and those produced by dominantly horizontal movements.  相似文献   

14.
Martian Topography: Scaling, Craters, and High-Order Statistics   总被引:1,自引:0,他引:1  
The high-order structure functions of Mars topography reveal three specific ranges of scales: (1) scaling range at small scales where the structure functions exhibit scaling behavior; (2) transition range where the structure functions continue to grow but do not reveal scaling; and (3) saturation range at large scales where the structure functions saturate. The scaling and saturation ranges are explored in detail in respect to scaling and intermittency. Analysis of the Mars Orbiter Laser Altimeter (MOLA) data and computer simulations suggest that there are two potential contributors to the small-scale scaling: (i) scale-invariant surface formation; and (ii) effects of discrete morphological forms such as craters. The crater effect also provides an explanation for the large-scale intermittency revealed using the normalized structure functions within the saturation range, which cannot be explained by the ‘scale-invariant’ concept. Overall, the obtained results suggest that the “crater” contribution to the structure function behavior often dominates over the effect of the scale-invariant surface formation.  相似文献   

15.
The paleomagnetic results obtained in 23 sites from red beds of the northern border of the inverted Cameros Basin (northern Iberian Peninsula) prove a Cretaceous widespread remagnetization. Paleomagnetic and rock magnetic analyses indicate that the Natural remanent magnetization (NRM) is dominated by a stable and always normal polarity component carried by haematite. Two conglomerate test and five-fold test indicate that this component is a syn-tectonic overprint dated between Albian and Santonian times, most probably Albian, contemporary with a low-grade metamorphism. Remagnetization was acquired before compressional deformation and post-dates the main extensional stage of basin formation (Berriasian–Albian). Incremental fold tests provide best clustering solutions showing dispersed results and far from the expected direction. An alternative procedure to obtain fold test solution was applied considering asymmetric limb rotation. Mean directions obtained from these “asymmetric solutions” are consistent with the expected direction and yield a statistical value for significant grouping at the 95% confidence level in all fold tests performed. This reconstruction allows to determine the tilting of beds at the moment of acquisition of magnetization. These original dips were used to reconstruct the original geometry of the northern basin border, later modified during the Tertiary inversion stage. This extensional geometry can be characterised as a large-scale syn-sedimentary normal fault drag, with a minor roll-over anticline. The procedure developed in this paper should be tested in other inverted basins that also have undergone burial remagnetizations.  相似文献   

16.
In this work, the recently developed “second-order” self-consistent method [Liu, Y., Ponte Castañeda, P., 2004a. Second-order estimates for the effective behavior and field fluctuations in viscoplastic polycrystals. J. Mech. Phys. Solids 52 467–495] is used to simulate texture evolution in halite polycrystals. This method makes use of a suitably optimized linear comparison polycrystal and has the distinguishing property of being exact to second order in the heterogeneity contrast. The second-order model takes into consideration the effects of hardening and of the evolution of both crystallographic and morphological texture to yield reliable predictions for the macroscopic behavior of the polycrystal. Comparisons of these predictions with full-field numerical simulations [Lebensohn, R.A., Dawson, P.R., Kern, H.M., Wenk, H.R., 2003. Heterogeneous deformation and texture development in halite polycrystals: comparison of different modeling approaches and experimental data. Tectonophysics 370 287–311], as well as with predictions resulting from the earlier “variational” and “tangent” self-consistent models, included here for comparison purposes, provide insight into how the underlying assumptions of the various models affect slip in the grains, and therefore the texture predictions in highly anisotropic and nonlinear polycrystalline materials. The “second-order” self-consistent method, while giving a softer stress-strain response than the corresponding full-field results, predicts a pattern of texture evolution that is not captured by the other homogenization models and that agrees reasonably well with the full-field predictions and with the experimental measures.  相似文献   

17.
18.
After describing attempts at perfecting a methodology for studying isotropic and anisotropic macroseismic fields in previous works, the authors here try to identify the causes of anisotropy in the context of the “new basement tectonics”.The seismic data are taken both from reconstructions of the macroseismic fields of historic events, by means of a critical analysis of the data, and from macroseismic fields of recent events surveyed by the authors. These data are correlated to the structural framework obtained through recent neotectonic studies and the lineament distribution traced on satellite images and using the “shadow” method. Generally the direction of elongation of the mesoseismic area is closely dependent on the source parameters and can be associated with recent and present-day systems outlined by the latest neotectonic studies.The best correlation is observed, however, with the lineament pattern obtained using the “shadow” method: the domains of the lineaments associated with the preferential trend of the macroseismic field show, in the rose diagram of cumulative number, values of prevalence and kurtosis higher than average; in the cumulative lengths diagram, on the other hand, they show prevalence maxima and, in particular, kurtosis maxima which are all the higher the more the anisotropic trend of field is accentuated. Using the “Giant Griffith Cracks” model for the lineaments, it can be deduced that the swarms refer to fracture systems with greater vertical development generated during the most recent tectonic phases.Finally, from a study of the dynamic characteristics of the elastic waves, that are the main agents responsible for macroseismic effects, it can observed that the wavelength order of magnitude is comparable with that of the linear parameters in the “warp” formed by the “Giant Cracks”. It can, thus, be deduced that the strong absorption of energy can be determined by the fracture swarm when the wave propagation occurs orthogonally to the swarm.  相似文献   

19.
The Neoproterozoic Katangan R.A.T. (“Roches Argilo-Talqueuses”) Subgroup is a sedimentary sequence composed of red massive to irregularly bedded terrigenous-dolomitic rocks occurring at the base of the Katangan succession in Congo. Red R.A.T. is rarely exposed in a continuous section because it was affected by a major layer-parallel décollement during the Lufilian thrusting. However, in a number of thrust sheets, Red R.A.T. is in conformable sedimentary contact with Grey R.A.T which forms the base of the Mines Subgroup. Apart from the colour difference reflecting distinct depositional redox conditions, lithological, petrographical and geochemical features of Red and Grey R.A.T. are similar. A continuous sedimentary transition between these two lithological units is shown by the occurrence of variegated to yellowish R.A.T. The D. Strat. “Dolomies Stratifiées” formation of the Mines Subgroup conformably overlies the Grey R.A.T. In addition, a transitional gradation between Grey R.A.T. and D. Strat. occurs in most Cu–Co mines in Katanga and is marked by interbedding of Grey R.A.T.-type and D. Strat.-type layers or by a progressive petrographic and lithologic transition from R.A.T. to D. Strat. Thus, there is an unquestionable sedimentary transition between Grey R.A.T. and D. Strat. and between Grey R.A.T. and Red R.A.T.The R.A.T. Subgroup stratigraphically underlies the Mines Subgroup and therefore R.A.T. cannot be comprised of syn-orogenic sediments deposited upon the Kundelungu (formerly “Upper Kundelungu”) Group as suggested by Wendorff (2000). As a consequence, the Grey R.A.T. Cu–Co mineralisation definitely is part of the Mines Subgroup Lower Orebody, and does not represent a distinct generation of stratiform Cu–Co sulphide mineralisation younger than the Roan orebodies.  相似文献   

20.
If the orientation of the principal compressive stress is oblique to layering, viscous multilayers fold in response to the layer-parallel shortening and develop asymmetric interfaces in response to the layer-parallel shear. A theoretical analysis of folding of viscous multilayers with different slip laws at layer contacts shows that the sense of asymmetry of folds is determined largely by the behavior of the layer contacts and the sense of layer-parallel shear during folding.

For a given sense of layer-parallel shear, the sense of asymmetry of folds can be reversed by changing only the behavior of the layer contacts. If the slip rate is linearly proportional to the shear stress at layer contacts, the resistance to slip is the same everywhere along interfaces, and the folds develop the sense of asymmetry of drag folds. If the slip rate is a nonlinear function of the shear stress at layer contacts, however, the resistance to slip varies with position along interfaces, and folds develop the sense of asymmetry of monoclinal kink folds.

For a given variable resistance to slip at layer contacts, the sense of asymmetry depends on the sense and magnitude of the layer-parallel shear and on the thickness-to-wavelength ratio of the multilayer.

For finite multilayers with variable resistance to slip at contacts, an increase in the layer-parallel shear stress decreases the dominant wavelength and increases the amplification factor for the initial perturbation of the interface.

The multilayer consists of linear viscous layers and is confined by thick, viscous media. Resistance to slip at layer contacts is modeled theoretically by a powerlaw relationship between rate of slip and contact shear stress. The equations, derived to 2nd order in the slopes of the interfaces, describe the growth of asymmetric folds from initial, symmetric perturbations.  相似文献   


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