分形褶皱复杂性的流变因素研究

根据Ramberg的纵弯褶皱粘性力学实验,在褶皱形态的分形分析基础上,利用分形理论和褶皱的流变学理论导出了褶皱的分数维(D)与岩层厚度(h)和粘度(μ)间的关系式,并探讨了褶皱复杂性对褶皱分数维的影响,从中获得有关复杂褶皱的流变学信息。影响分形褶皱复杂程度的因素很多,主要因素包括岩层的厚度和粘度。因此,对褶皱的分形测量和岩层厚度及粘度的分析,可以定量分析分形褶皱形成的流变机理。这一研究是褶皱的非线性流变学理论研究的一个尝试。     

Impact of mechanical anisotropy and power-law rheology on single layer folding

The infinitesimal and finite stages of folding in nonlinear viscous material with a layer-parallel anisotropy were investigated using numerical and analytical methods. Anisotropy was found to have a first-order effect on growth rate and wavelength selection, and these effects are already important for anisotropy values (normal viscosity/shear viscosity) < 10. The effect of anisotropy must therefore be considered when deducing viscosity contrasts from wavelength to thickness ratios of natural folds. Growth rates of single layer folds were found to increase and subsequently decrease during progressive deformation. This is due to interference between the single layer folds and chevron folds that form in the matrix as a result of instability caused by the anisotropic material behaviour. The wavelength of the chevron folds in the matrix is determined by the wavelength of the folded single layer, which can explain the high wavelength to thickness ratios that are sometimes found in multilayer sequences. Numerical models including anisotropic material properties allow the behaviour of multilayer sequences to be investigated without the need for resolution on the scale of individual layers. This is particularly important for large-scale models of layered lithosphere.     

岩体结构对含煤岩系变形的控制作用

含煤岩系变形规律的研究,对煤炭资源评价和开采、煤矿瓦斯灾害预测、煤层气的可开发性评价具有指导意义。基于含煤岩系的岩体结构是控制其变形的基础因素这一前提,以岩体力学和分形几何学基本理论为指导,提出取决于岩石杨氏模量和泊松比的岩体强度因子和取决于岩层厚度的分形维数两个参数,以断层发育的安阳双全井田、褶皱发育的沁水盆地煤层气开发区及滑动构造发育的荥巩谷山井田为例,系统探讨了岩体结构对含煤岩系变形的控制作用。研究表明,低强度因子和厚层岩层较多的分形维数低值区,含煤岩系以韧性变形为主,多形成褶皱,煤体变形程度深,为瓦斯灾害严重区和煤层气难以开发区;高强度因子和厚层岩层较少的分形维数高值区,含煤岩系以脆性变形为主,多发育断层,构造煤难以区域展布,只分布在断层附近。可见含煤岩系变形不仅与岩体强度有关,而且受岩层厚度的控制。统计层段内刚性岩层的存在增加了岩体强度,岩层复杂程度的增加同样提高了岩体强度。岩体力学和分形几何学的引入,为煤岩体变形行为和程度的描述和预测提供了一种新途径。     

A theory of concentric, kink, and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: I. Introduction

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.     

Parallel, similar and constrained folds

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.     

Numerical modelling of finite-amplitude similar folds developing under general deformation histories

A simple model of similar folds in homogeneous materials with anisotropic properties is proposed and it is shown that the model is applicable to a wide range of natural examples of folds. A mathematical derivation is given which allows the instantaneous deformation of the folds to be calculated for any imposed bulk deformation. A means of projecting the effects of the deformation over a finite time interval is described. The modelling is illustrated by simulations of folds observed in the Morcles nappe, western Switzerland, based on the assumption that the folds formed under simple shear bulk deformation. Folds with geometrical features remarkably similar to those natural folds are produced in the modelling by varying the parameters.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: VI. Asymmetric folding and monoclinal kinking

One of the rules of thumb of structural geology is that drag folds, or minor asymmetric folds, reflect the sense of layer-parallel shear during folding of an area. According to this rule, right-lateral, layer-parallel shear is accompanied by clockwise rotation of marker surfaces and left-lateral by counterclockwise rotation. By using this rule of thumb, one is supposed to be able to examine small asymmetric folds in an outcrop and to infer the direction of axes of major folds relative to the position of the outcrop. Such inferences, however, can be misleading. Theoretical and experimental analyses of elastic multilayers show that symmetric sinusoidal folds first develop in the multilayers, if the rheological and dimensional properties favor the development of sinusoidal folds rather than kink folds, and that the folded layers will then behave much as passive markers during layerparallel shear and thus will follow the rule of thumb of drag folding. The analyses indicate, however, that multilayers whose properties favor the development of kink folds can produce monoclinal kink folds with a sense of asymmetry opposite to that predicted by the rule of thumb. Therefore, the asymmetry of folds can be an ambiguous indicator of the sense of shear.The reason for the ambiguity is that asymmetry is a result of two processes that can produce diametrically opposed results. The deformation of foliation surfaces and axial planes in a passive manner is the pure or end-member form of one process. The result of the passive deformation of fold forms is the drag fold in which the steepness of limbs and the tilt of axial planes relative to nonfolded layering are in accord with the rule of thumb.The end-member form of a second process, however, produces the opposite geometric relationships. This process involves yielding and buckling instabilities of layers with contact strength and can result in monoclinal kink bands. Right-lateral, layer-parallel shear stress produces left-lateral monoclinal kink bands and left-lateral shear stress produces right-lateral monoclinal kink bands. Actual folds do not behave as either of these ideal end members, and it is for this reason that the interpretation of the sense of layer-parallel shear stress relative to the asymmetry of folds can be ambiguous.Kink folding of a multilayer with contact strength theoretically is a result of both buckling and yielding instabilities. The theory indicates that inclination of the direction of maximum compression to layering favors either left-lateral or right-lateral kinking, and that one can predict conditions under which monoclinal kink bands will develop in elastic or elastic—plastic layers. Further, the first criterion of kink and sinusoidal folding developed in Part IV remains valid if we replace the contact shear strength with the difference between the shear strength and the initial layer-parallel shear stress.Kink folds theoretically can initiate only in layers inclined at angles less than to the direction of maximum compression. Here φ is the angle of internal friction of contacts. For higher angles of layering, slippage is stable so that the result is layer-parallel slippage rather than kink folding.The theory also provides estimates of locking angles of kink bands relative to the direction of maximum compression. The maximum locking angle between layering in a nondilating kink band and the direction of maximum compression is . The theory indicates that the inclination of the boundaries of kink bands is determined by many factors, including the contact strength between layers, the ratio of principal stresses, the thickening or thinning of layers, that is, the dilitation, within the kink band, and the orientation of the principal stresses relative to layering. If there is no dilitation within the kink band, the minimum inclination of the boundaries of the band is to the direction of maximum compression, or to the direction of nonfolded layers. Here α is the angle between the direction of maximum compression and the nonfolded layers. It is positive if clockwise.Analysis of processes in terminal regions of propagating kink bands in multilayers with frictional contact strength indicates that an essential process is dilitation, which decreases the normal stress, thereby allowing slippage and buckling even though slopes of layers are low there.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: VII. development of folds within Huasna Syncline, San Luis Obispo County, California

Folds in the Huasna area of the southern Coast Ranges of California provide an opportunity to study different fold forms and to estimate dimensional and relative rheological properties of rocks at the time of folding. Plunging, concentric-like and chevron-like folds with wavelengths ranging from about 0.1 to 1 km are clearly visible in natural exposures at the south end of the Huasna syncline, which has a wavelength of 12–16 km. Examination of two fresh roadcut exposures in the Miocene Monterey Formation suggests that folding within part of the Monterey was accommodated primarily by layer-parallel slip between structural layers with thicknesses ranging from 30 to 43 m, even though lithologic layers range from a few mm to a few dm in thickness. This part of the Monterey is folded into a series of concentric-like folds, with chevron-like folds at their cores and with a ratio of wavelength to total thickness of layers of about . Theoretical analysis of multilayers, comprised of identical, elastic or elastic—plastic layers with frictionless contacts, indicates that the effective, or weighted-average thickness of structural layers corresponding with an ratio of 0.42 is about 41 m. Thus, the theoretical predictions are roughly in agreement with available data concerning these folds.Thicknesses of structural units in other folds of this area are inadequately known to closely check theoretical predictions, but most of the data are consistent with predictions. An exception is the Huasna syncline which has a larger wavelength than we would predict. There are several likely explanations for this discrepancy. Layers in the underlying Franciscan complex may have taken part in the folding, making our estimates of total thickness too small. The basement rocks may have been much softer, relative to the overlying sedimentary rocks, than we assumed. The Huasna syncline could be partly a result of gravitational instability of relatively low density, Miocene siliceous and porcelaneous shales, overlain by relatively high density, Pliocene sandstones.The Huasna syncline and some of the smaller folds in the Miocene rocks are doubly in the northwest—southeast direction. Further, the maximum compression was approximately normal to the traces of the large faults in this part of California.     

基于强度折减法的土石混合体边坡长期稳定性研究

土石混合体边坡是自然界中常见的一种边坡类型,具有明显的不均匀性和不连续性。土体的蠕变是造成土石混合体边坡变形及失稳的主要原因之一,而目前关于土石混合体边坡稳定性的研究几乎均未考虑土体的蠕变性。首先运用数字图像处理技术对我国某水电站库区的一个土石混合体边坡进行建模,而后利用FLAC3D软件中的强度折减法对其进行稳定性分析,并着重研究了土体的蠕变特征及其蠕变参数对土石混合体边坡变形及稳定性的影响。计算结果表明,土体的蠕变特征会明显降低土石混合体边坡的安全系数,增大边坡变形,进而对边坡的稳定性造成不利影响;其中蠕变黏性系数对边坡的长期稳定性具有较大影响,黏性系数越大,则土石混合体边坡的安全系数越低。     

Re-folded structure of syn-orogenic granitoids(Padrón dome,NW Iberia):Assessing rheological evolution of cooling continental crust in a collisional setting

This contribution discusses about the rheological, kinematic and dynamic frameworks necessary to produce recumbent and upright folds from syn-orogenic granitic massifs that were formed during an early stage of magma genesis related to the onset of a migmatitic dome. Syn-kinematic granitoids occurring within the high-grade infrastructure of the Padron migmatitic dome(NW Iberia) are deformed into largescale recumbent folds(D_2) that are later affected by upright folds(D_3). Petrostructural analysis of a selected area of this dome reveals that after a period of crustal thickening(D_1), NNW-directed extensional flow gave way to recumbent folds and penetrative axial plane foliation(S_2). Superimposed subhorizontal compression resulted in upright folds(D_3). A closer view into the dynamics of the dome allows exploring the factors that may condition the nucleation of folds with contrasting geometries during progressive deformation of molten continental crust. The formation of folds affecting syn-kinematic granitoids suggests a cooling metamorphic path in migmatitic domes. Active and passive folding mechanisms require a crystallizing(cooling) magma to nucleate folds. A more competent metamorphic host inhibits fold nucleation from much less competent magmas. As it crystallizes, magma becomes more rigid(competent),and approaches viscosity values of its host. Passive folding is favored when no significant competence contrast exists between magma and host, so this folding mechanism is more likely shortly after magma genesis and emplacement. In such conditions, and under dominant subhorizontal flow accompanied by flattening(D_2),passive folding would produce isoclinal recumbent geometries. Further magma cooling introduces a shift into the rheological behavior of partially molten crust. Thereon, crystallizing magma bodies would represent significant competence contrasts relative to their host. At this point, buckling is a more likely folding mechanism, and more regular, buckle folds re-fold previous structures after significant cooling. The geometry of resulting folds is upright due to dominant subhorizontal compression(D_3) at this stage.     

样子哨盆地构造演化特征

样子哨盆地基底为龙岗地块,盖层以晚元古代地层、古生代地层为主。基底构造变形以韧塑性变形和塑性纵弯柔流褶皱及固态流变剪切变形为主,发生片理、片麻理、褶皱及条带状构造。盖层经历多次挤压隆升和拉张断陷运动,屡次遭受海侵—海退,沉积了典型的地台型沉积建造。后经断块运动,改造或继承先期断裂,形成盆地—山岭式构造。     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: V. asymmetric folding in interbedded chert and shale of the franciscan complex, san francisco bay area, california

The origin of tight, asymmetric, kink-like or chevron-like folds in interbedded shales and radiolarian cherts of the Franciscan Complex in the San Francisco Bay area has been somewhat of a mystery for many years. Stephenson Ellen provided many clues as to the origin and indicated that the folds became asymmetric as a result of layer-parallel shear. He believed that the original folds were conjugate kink folds.As a result of reexamination of most of the folds studied by Ellen, of experimentation with elastic multilayers and of the theories developed in Parts III and IV of this series of papers, we believe that the original folds were mostly chevron rather than kink folds. Thus, we suggest that the folds formed by a combination of layer-parallel shortening and layer-parallel shear when the rocks were soft and pore pressures were high.Several lines of evidence suggest that typical folds in the Franciscan are asymmetric chevron folds. A combination of theory of finite simple shear and of experimentation with elastic multilayers indicates that the tight folds of the Franciscan could have been produced by smaller angles of simple shear if the original folds were typical chevron folds rather than typical kink folds. Several field observations, including thickening of shales but not of cherts in hinges of folds and lack of deformation of radiolaria in the cherts, indicate that the cherts were soft and the shales very soft at the time of folding. The pore-water pressures in the shales probably were high. Such conditions theoretically favor concentric-like and chevron folding, not kink folding. Finally, most of the asymmetric folds in a quarry exposure can be reconstructed geometrically as typical chevron folds but not as typical kink folds subjected to simple shear.     

Layer shortening and fold-shape development in the buckling of single layers

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 (μ_layer/μ_host = μ₁/μ₂) 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 μ₁/μ₂ = 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 μ₁/μ₂ = 10, and in experiments for μ₁/μ₂ = 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.     

The impact of cover rock rheology on the style of folding in the Zagros fold-thrust belt

The present day morphology of the Zagros fold-thrust belt is dominated by magnificent exposures of NW–SE trending folds. These folds differ in their size and geometry and these differences are related mainly to the rheological profile of the cover rock. The cover rock succession of the Zagros consists of a sequence of competent and incompetent units which vary both along and across the belt. Field based study combined with the use of satellite images reveals that the thickness and facies distribution of the cover rock succession has a significant impact on the style of deformation. During the shortening linked to the current convergence of the Arabian and Iranian plates, the incompetent units act as detachment horizons which localise thrusting and which act as décollement above which detachment folds form. In addition, where these incompetent units are thick (e.g.> 1 km), they allow the deformation above and below them to become completely decoupled enabling disharmonic folding to occur. As a result the folds above and below the incompetent units in the central part of the Zagros Folded Belt, have significantly different geometries and wavelengths. As the Zagros folds host the majority of the hydrocarbon reserves in Iran and Iraq, an understanding of the processes that influence their geometry and spatial organization at different levels in the cover rock is crucial for the future exploration in the region.     

川东南马尾状褶皱带特征与形成机制的物理模拟

川东南地区是我国南方重要的天然气探区,气藏分布受与该区的褶皱带构造演化密切相关.该区褶皱带呈现马尾状平面构造样式,对于这种特殊褶皱样式的形成机制存在不同的观点.构造物理模拟是研究构造形成机制的有效手段.为此,笔者在对该区马尾状褶皱特征详细分析的基础上,设计了5组模型,分别考虑边界几何形态、地层流变学结构、韧性层粘度和基底摩擦系数等4个因素,对该褶皱带的形成机制开展系统研究.结果表明:（1）该区马尾状褶皱带的形成与川东华蓥山断裂和齐岳山边界断裂形态关系密切;（2）脆/韧性地层厚度比和脆性层的厚度差对褶皱波长和样式具有重要控制作用;（3）适当的基底摩擦力是形成马尾状褶皱带的重要条件;（4）四川盆地内部、川东地区和湘鄂西地区基底流变学强度差异对该区马尾状褶皱带也具有重要影响.      

软沉积物滑塌变形物理模拟及变形机理分析*

软沉积物滑塌变形是一种地质现象,对于分析区域地质发展史和指导油气勘探具有重要的意义,近年来越来越受到地学界的重视。但大多数的研究是基于野外现象的定性观察描述,对其形成过程和成因机制的定量探究较少。笔者建立了一套斜坡背景下重力驱动的软沉积物滑塌变形物理模拟实验装置,并设计了完整的实验程序,利用具有不同黏滞系数的材料模拟地层,通过多次实验改变沉积箱坡度模拟不同的地层倾角,总结了软沉积物滑塌变形的演化模式: 滑塌开始,模拟地层逐渐隆起;随着地形坡度变大,滑塌褶皱依次发展成圆弧褶皱、紧密等斜褶皱,断裂产生后形成类似无根等斜褶皱和鞘褶皱的变形构造,直到地层趋于平稳。分析了软沉积物滑塌变形的机理: 软沉积物受到自身沿斜坡重力的驱动,发生滑塌,层与层之间的剪切效应导致软沉积物发生变形。     

Coeval folding and boudinage under plane strain with the axis of no change perpendicular to the layer

Plane-strain coaxial deformation of a competent plasticine layer embedded in an incompetent plasticine matrix was carried out to improve our understanding about the evolution of folds and boudins if the layer is oriented perpendicular to the Y-axis of the finite strain ellipsoid. The rock analogues used were Beck’s green plasticine (matrix) and Beck’s black plasticine (competent layer), both of which are strain-rate softening modelling materials with a stress exponent n=ca. 8. The effective viscosity η of the matrix plasticine was changed by adding different amounts of oil to the original plasticine. At a strain rate of 10⁻³ s⁻¹ and a finite strain e of 10%, the effective viscosity of the matrix ranges from 1.2×10⁶ to 7.2×10⁶ Pa s. The effective viscosity of the competent layer has been determined as 4.2×10⁷ Pa s. If the viscosity ratio is large (ca. 20) and the initial thickness of the competent layer is small, both folds and boudins develop simultaneously. Although the growth rate of the folds seems to be higher than the growth rate of the boudins, the wavelength of both structures is approximately the same as is suggested by analytical solutions. A further unexpected, but characteristic, aspect of the deformed competent layer is a significant increase in thickness, which can be used to distinguish plane-strain folds and boudins from constrictional folds and boudins.An erratum to this article can be found at     

引入非线性瞬时弹性模量的软土流变模型

软土是一种非线性流变物质,但现行流变模型却忽略了加载瞬时的非线性变形;软土流变试验参数是数学模型参数而非物理模型参数,一个土样一般只对应一种材料参数,但现行流变模型的模型参数常随着荷载变化,且变化无规律,离散性大。基于以有机质为流变相物质的人工土试样室内一维压缩蠕变试验,建立了各级荷载作用下具有相同模型参数的7组件流变模型,用非线性弹簧H描述软土加载瞬时弹塑性变形、并联的三元件组件模拟软土随时间变化的黏弹塑变形。结果表明：引入三次非线性瞬时弹性模量的7组件流变模型能够较准确地反映软土的流变特性。     

混凝土面板堆石坝堆石料流变特性试验研究

采用大型三轴仪对公伯峡水电站面板堆石坝坝内3种主要堆石料的流变特性进行了试验研究,分析了堆石料流变的影响因素,重点研究了应力状态对流变的影响,探讨了流变的规律性,发现堆石料的流变随时间呈指数型衰减,符合Merchant模型描述的变形规律。研究了堆石体流变模型,提出了最终体积流变和最终剪切流变的表达式。