Flow through anisotropic networks

This paper presents an analysis of Hagen-Poiseulle flow through plane random anisotropic networks of interconnected channels. Macroscopic permeability tensor of the network is expressed in terms of statistico-geometrical characteristics like the degree of anisotropy in channel orientations, average co-ordination number of the network and first two moments of channel length distribution. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. The emphasis of the paper is on the effects of anisotropy on distributions of flow rates in channels. It is shown that, due to anisotropy the maximum flow rate generally occurs in channels that are not aligned along the direction of the macroscopic pressure gradient.     

Flow through anisotropic networks

This paper presents an analysis of Hagen-Poiseulle flow through plane random anisotropic networks of interconnected channels. Macroscopic permeability tensor of the network is expressed in terms of statistico-geometrical characteristics like the degree of anisotropy in channel orientations, average co-ordination number of the network and first two moments of channel length distribution. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. The emphasis of the paper is on the effects of anisotropy on distributions of flow rates in channels. It is shown that, due to anisotropy the maximum flow rate generally occurs in channels that are not aligned along the direction of the macroscopic pressure gradient.     

裂隙土等效连续介质的渗透张量及表征单元体积

裂隙土的渗透特性是裂隙土边坡稳定性分析中重要的参数。文中通过分别考虑随机裂隙网络和土体本身的渗透性,推导裂隙土的渗透系数,并用张量的形式表示渗透系数的各向异性。同时建立了确定裂隙土表征单元体积的准则,为应用等效连续介质模型提供了基础。结果表明裂隙土的渗透系数大于裂隙网络和土体的渗透系数,其渗透方向取决于裂隙网络的渗透方向。算例中裂隙土的表征单元体积大约是裂隙长度平均值的5倍。     

中国数字地震台网(CDSN)单台站P波偏振分析

偏振分析可以定量描述地震波的质点运动。 P波质点运动在水平方向上发生偏振, 使得传播方向会偏离台站与地震震源之间大圆弧的方向。 P波偏振分析可以用来约束地下结构以及反映地震各向异性, 提供与剪切波分裂等手段不同的证据。 本文介绍并使用主成分分析(Principle Component Analysis, PCA)的方法, 计算了单一地震台的P波偏振, 同时, 利用谐和分析, 对台站下方的各向异性进行了分析。 将P波偏振分析应用到中国数字地震台网(China Digital Seismograph Network, CDSN)的四个台站10年左右的数据, 筛选并分析了震相清晰、 信噪比高的远震三分量初至P波的质点运动, 拟合出四个台站接收到的地震事件后方位角与P波水平偏离角度之间的三角函数曲线, 计算出拉萨台、 昆明台下方上地幔各向异性的偏振方向分别为66°和57°, 大致呈现北东东方向。     

Porosity of bimodal and trimodal sediment mixtures

This study focuses on the prediction of the porosity of nonuniform sediment mixtures,considering the effects of particle packing.A random particle packing model has been developed for the porosity of bimodal mixtures by extending the existing random particle filling theory.Coefficients in the developed model are calibrated by fitting the model to measured data for a variety of bimodal mixtures,including spherical glass particles,rounded quarry grains,and natural sediments.The model coefficients ...     

New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity

 Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy, that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy, i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient. It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions. In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its implementation with numerical simulations.     

New methods for measuring the permeability of rock samples for a single-phase fluid

A complex of methodology, instrumentation, and software tools is worked out, which makes it possible to accomplish high-precision measurements of permeability for a single-phase fluid and its anisotropy within a wide range of values both under the normal conditions and high temperature and pressure.The transient method, modified with allowance for the dependence of the properties of a percolating gas on the parameters of its state, enables one to simultaneously determine, from the data of a single experiment, the permeability values for a sample of condensed fluid and the Klinkenberg constant, which characterizes the pore space of rock. This approach made it possible to substantially increase the accuracy of measurements, reducing their labor-intensiveness.The method of varying the flow shape makes it possible to simultaneously determine, in the course of a single experiment, the axial and radial components of the permeability tensor of anisotropic rocks with layered structure. The instrumentation and software implementing these new methodologies are developed and thoroughly tested.     

Laboratory and theoretical evaluation of impact of packing density,particle shape,and uniformity coefficient on erodibility of coarse-grained soil particles

Sedimentation – including erosion, transport, and deposition of coarse-grained particles – is a primary and growing environmental, engineering, and agricultural issue around the world. Soil erosion occurs when the hydrodynamic force induced by flowing water exceeds the geotechnical resistance of soils, as measured by critical shear stress for initiation of soil-particle motion. Even though various quantitative methods have been suggested with respect to different types of soil, the most widely accepted formula to estimate critical shear stress for coarse-grained soil is a direct function of the median grain size of the soil particles; however, the erosion resistance of soils also varies with other geotechnical properties, such as packing density, particle shape, and uniformity coefficient. Thus, in this study, a combined rolling–lift model for particle detachment was derived based on theoretical analysis. A series of experimental flume tests were conducted with specimens prepared with standard soil types, as well as laboratory-prepared mixtures of coarse-grained soil to validate the theoretical model and determine the effect of other geotechnical properties on the erosion characteristics of coarse grains, coupled with the effect of median particle size. The results indicated that the median grain size is the primary variable determining the resistance of coarse grains, but the critical shear stress also varies with the packing density of the soil matrix. In addition, angular particles show more erosion resistance than rounded particles, and the erosion potential of a soil decreased when the grain is well graded (higher value of uniformity coefficient). Additionally, regression analysis was performed to quantify the effect of each parameter on the critical shear stress of coarse grains. © 2020 John Wiley & Sons, Ltd.     

Influence of magnetic interactions on the anisotropy of magnetic susceptibility: the case of single domain particles packed in globule aggregates

The influence of magnetic interactions on the anisotropy of magnetic susceptibility (AMS) have been largely studied by several theoretical models or experiments. Numerical models have shown that when magnetostatic interactions occur, the distributions of particles over the volume rather than their individual orientations control the AMS. We have shown recently from a comprehensive rock magnetic study and from a theoretical 2-dimensional (2-D) model that single domain particles closely packed in globule aggregates could produce strong local random interaction magnetic fields which could influence the magnetic susceptibility and decrease the degree of anisotropy. In this paper, we first present in detail this 2-D theoretical model and then we extend it to the 3-D case. The possible distribution function of the magnetostatic interaction fields comprises two extreme states: it is either isotropic or ordered. The former case corresponds to the thermal-demagnetized state while the second case corresponds to the alternating field (AF) demagnetized state. We show that when easy axes of magnetization are not uniformly distributed, the degree of anisotropy decreases as the interaction field increases in both AF- and thermal-demagnetized states in 2-D and 3-D geometry. Thus we conclude that random magnetic fields generated by a random arrangement of magnetic particles over the sample volume decrease the degree of anisotropy of AMS and may alter the magnetic fabric.     

The stable orientations of the net magnetic moment within single-domain particles: Experimental evidence for a range of stable states and implications for rock magnetism and palaeomagnetism

An idealised stable uniaxial single-domain (SD) particle permits only two possible stable positions in which the magnetic moment can lie, either closely parallel or anti-parallel to the particle long (easy) axis. In real acicular SD particles, which have generally been regarded as uniaxial, this implicit two state feature has never been challenged, whilst there has been considerable debate concerning the mechanism of moment reversal between the two states. We present experimental results suggesting that acicular SD particles may actually have a range of several quantifiable stable (or metastable) orientations of the net magnetic moment. In order to help explain our experimental observations we present a new simple model of acicular SD particles, which gives quantitative predictions verified by further experiments. The model also appears to be relevant to other SD particle morphologies and crystal structures (such as hematite). A possible physical basis for our model in acicular particles may lie in non-uniform SD structures (such as the flower or vortex states). Small variations in the non-uniform SD structures available to a particle might allow a range of stable positions of the net moment.The results have several implications for rock magnetism and palaeomagnetism. Firstly, the new model can quantitatively account for several previously unexplained diverse phenomena exhibited by real acicular SD particles. These include the acquisition of gyroremanences and field-impressed anisotropy in dilute dispersions of such particles, as well as observations of transverse components of remanence in individual acicular SD particles. All these phenomena are theoretically impossible in idealised uniaxial SD particles. Interestingly, it appears that these phenomena could now be used to quantify the deviation of real acicular SD particles from ideal uniaxial behaviour and also, therefore, the deviation from a uniform SD structure. In hematite, observations of large field-impressed anisotropy appear to be quantitatively explained by the available positions of the moment in the basal plane.Secondly, computations of the ancient field vector and palaeointensity from remanence anisotropy techniques would not only be controlled by the shape and distribution of the particles, but also by the range of possible stable orientations of the net moment within each SD particle. Laboratory analogue remanences (and, we suspect, natural remanences) would be influenced by the range of possible stable moment positions. Quantifying the range of these stable moment positions, upon acquisition of laboratory or natural remanences, should lead to improved methods of computing the ancient field direction and palaeointensity in anisotropic rocks.     

The yield strength of subliquidus basalts — experimental results

Yield strength is an important property of particle–fluid suspensions. In basaltic lavas that crystallize during flow emplacement, the onset of yield strength may result in threshold transitions in flow behavior and flow surface morphology. However, yield strength–crystallinity relations are poorly known, particularly in geologic suspensions, where difficulties of experimental and field measurements have limited data acquisition in the subliquidus temperature range. Here we describe two complementary experimental approaches designed to examine the effect of particle shape on the low-shear yield strength of subliquidus basalts. The first involves melting cubes of holocrystalline basalt samples with different initial textures to determine the temperature (crystallinity) at which these samples lose their cubic form. These experiments provide information on the minimum crystal volume fractions (0.20<φ<0.35) required to maintain the structual integrity of the cube. The second set of experiments uses suspensions of corn syrup and neutrally buoyant particles to isolate the effect of particle shape on yield strength development. From these experiments, we conclude that the shape is important in determining the volume fraction range over which suspensions exhibit a finite yield strength. As anisotropic particles may orient during flow, the effect of particle shape will be controlled by the orientation distribution of the constituent particles. We find that the so-called ‘excluded volume’ can be used to relate results of experiments on anisotropic particles to those of suspensions of spherical particles. Recent measurements of yield strength onset in basaltic melts at crystal volume fractions near 0.25 are consistent with our observations that crystal frameworks develop at low to moderate crystal volume fractions when crystals are anisotropic (e.g. plagioclase). We further suggest that conditions leading to yield strength onset at low crystallinities include rapid cooling (increased crystal anisotropy), heterogeneous nucleation (which promotes extensive crystal clustering and large cluster anisotropy) and static conditions (random crystal orientations).     

改进的各向异性标准化方差探测斜磁化磁异常源边界

针对存在强剩磁作用磁化方向不明的磁异常,本项研究探索直接处理斜磁化磁异常的识别,提出了基于磁力梯度张量模的各向异性边界探测方法.首先利用各向异性尺度改进了各向异性标准差的核函数,突出各向异性高斯函数的作用;结合磁力梯度张量模来消弱斜磁化的影响.数值实验模拟了一组复杂磁异常模型,在斜磁化条件下分析该研究方法的边界探测效果.实验表明：改进方法,即磁力梯度张量模的各向异性标准化方差,它可以探测非垂直磁化磁异常的磁源边界;同时指出,改进方法比基于三维解析信号振幅的各向异性标准化方差对磁化方向的依赖性更小.将该方法应用于中国西部某磁铁矿集区的精细探测,在非垂直磁化条件下对实测磁异常直接进行边界探测,获得了较为理想的处理结果.     

Image analysis and circular statistics for shape-fabric analysis: applications to lithified ignimbrites

 Computer-assisted image analysis can be successfully used to derive quantitative textural data on pyroclastic rock samples. This method provides a large number of different measurements such as grain size, particle shape and 2D orientation of particle main axes (directional- or shape-fabric) automatically and in a relatively short time. Orientation data reduction requires specific statistical tests, mainly devoted to defining the kind of particle distribution pattern, the possible occurrence of preferred particle orientation, the confidence interval of the mean direction and the degree of randomness with respect to pre-assigned theoretical frequency distributions. Data obtained from image analysis of seven lithified ignimbrite samples from the Vulsini Volcanic District (Central Italy) are used to test different statistics and to provide insight about directional fabrics. First, the possible occurrence of a significant deviation from a theoretical circular uniform distribution was evaluated by using the Rayleigh and Tukey χ ² tests. Then, the Kuiper test was performed to evaluate whether or not the observation fits with a unimodal, Von Mises-like theoretical frequency distribution. Finally, the confidence interval of mean direction was calculated. With the exception of one sample (FPD10), which showed a well-developed bimodality, all the analysed samples display significant anisotropic and unimodal distributions. The minimum number of measurements necessary to obtain reasonable variabilities of the calculated statistics and mean directions was evaluated by repeating random collections of the measured particles at increments of 100 particles for each sample. Although the observed variabilities depend largely on the pattern of distribution and an absolute minimum number cannot be stated, approximately 1500–2000 measurements are required in order to get meaningful mean directions for the analysed samples. Received: 9 April 1996 / Accepted: 26 December 1996     

医用CT在三维椭球颗粒随机堆积结构研究中的应用

颗粒随机堆积问题是物理和工程领域的热门问题。椭球颗粒随机堆积体系作为球形体系的拓展,增加了旋转自由度,从而表现出更复杂的性质,由于椭球颗粒比球形颗粒更类似于自然界中普遍存在的非规则颗粒,因此其研究具有重要的实用价值。研究三维颗粒堆积结构问题一般需要CT成像技术,本文介绍了如何利用医用CT对三维椭球随机堆积体系进行成像研究的技术细节,包括如何通过图像处理的方法获取椭球颗粒的空间位置、取向和体积,如何利用接触数标度函数拟合的方法得到近邻颗粒间的接触信息等。本文的研究内容和方法为利用各种X射线CT成像方法研究三维颗粒体系提供了技术参考。      

Dielectric anisotropy and fabric of rocks

Summary Measurements have been made of the dieletric anisotropies of a number of rocks for which magnetic anisotropy data have been obtained previously. The purpose was to examine the possible usefulness of dielectric anisotropy as a physical property indicative of rock fabrics. Its advantage over the magnetic method is that it measures an average alignment of crystals of the dominant minerals, whereas magnetic anisotropy is due only to the ferromagnetic grains. Disadvantages are an extreme sensitivity to specimen shape and difficulty in distinguishing the several types of alignment which can give rise to dielectric anisotropy. In a number of strongly foliated rocks the axes of dielectric anisotropy were found to coincide with the axes of magnetic anisotropy. Specimens from a magnesian-pyroxene rich layer in a Tasmanian dolerite sill and from the olivine rich layer of the Palisades dolerite sill, New York, were found to have no systematic anisotropy. The pyroxenes in the Tasmanian dolerite are elongated crystals (about 2: 1) so that the dielectric measurements show that they do not have a preferred horizontal alignment and therefore have probably not settled as individual crystals. Most of the olivines in the Palisades dolerite are more nearly equidimensional so that the absence of measurable anisotropy in this rock is less conclusive evidence against crystal settling.     

Solar proton event in December 2006

The variations in the rigidity spectrum and anisotropy of cosmic rays in December 2006 have been studied based on the surface measurements of the cosmic ray intensity at the global network of stations, using the method of global spectrographic survey. It has been indicated that the highest degree of anisotropy (to ～50%) with the maximal intensity of particles with a rigidity of 4 GV in the direction from the Sun (an asymptotic direction of about ?25° and 160°) was observed at 0400 UT on December 13. The parameters of the cosmic ray rigidity spectrum, which reflect the electromagnetic characteristics of the heliospheric fields during the studied period, have been determined when the surface and satellite measurements of protons in the energy range from several megaelectronvolts to several tens of gigaelectronvolts were jointly analyzed. The observed anisotropy and variations in cosmic rays in a wide energy range have been explained based on an analysis of the results.     

Observation of azimuthal anisotropy from the seismic reflectivity of a Tertiary turbidite sand

P‐wave data from a time‐lapse 3D OBC survey have been analysed to estimate and interpret azimuthal seismic anisotropy. This is achieved by careful processing to preserve the azimuthal signature. The survey images a major reservoir body in a channelized turbidite field in the Gulf of Mexico. Three distinct and significant anisotropy anomalies are discovered on or around this particular ‘4500‐ft sand’, all of which change intensity but not orientation with hydrocarbon production. These anomalies are distributed along the highest concentration of cumulative sand thickness, with their symmetry axes aligned with the main channel axis. We suspect that this time‐lapse anisotropy could be caused by the alignment of the depositional grain fabric. Theoretical calculation predicts that this mechanism, when combined with fluid‐saturation changes, can generate the observed pattern of behaviour. If further supported by other researchers, this result would indicate that appropriately designed seismic surveys could be a useful tool for palaeo‐direction studies in clastic reservoirs and also a useful constraint for directional permeability in the reservoir flow simulation model.     

DARCY'S COEFFICIENT OF PERMEABILITY AS SYMMETRIC TENSOR OF SECOND RANK

Synopsis

The dynamic equation of motion that governs the laminar flow of water through soils is the empirical equation of Darcy. According to Darcy's equation the velocity of the flowing water is proportional to the hydraulic gradient under which the water is flowing, with the constant of proportionality being the coefficient of permeability. The interesting question arising is whether or not the coefficient of permeability is a scalar quantity (having only a magnitude) or a vector (having both magnitude and direction). It is proved, in the present paper, that the permeability coefficient is neither a scalar nor a vector but a symmetric tensor of second rank. The fact that the permeability tensor is symmetric gives rise to great simplifications and permits a simple graphical construction of the tensor ellipsoid. Having the tensor ellipsoid, the determination of the direction at which the water will flow under a known imposed hydraulic gradient can be found graphically. In case of isotropic soils (the permeability coefficient has the same value along any direction) the ellipsoid reduces to a sphere and the tensor becomes a scalar. In the general case of anisotropic soils the permeability tensor is an entity with nine elements, six of which are independent representing pure extension or contraction along the three principal coordinate axes, thus transforming the permeability sphere into an ellipsoid and vice versa. It should be noted that in anisotropic soils the only directions along which the flow takes place in the direction of the hydraulic gradient are those of the principal axes of the tensor ellipsoid.

Permeability tests were conducted on anisotropic sandstone samples taken at different directions with respect to rectangular coordinates. The permeability coefficient values plotted on a two-dimensional polar coordinate graph paper give rise to an ellipse substantiating therefore the tensor concept of the permeability coefficient. The graphical construction of the tensor ellipse and the use of it in order to obtain the direction of flow by knowing the direction of the hydraulic gradient is also shown.     

A search for flow structure in columnar basalt using magnetic anisotropy measurements

Summary Evidence for flow structure within hexagonal columns of basalt has been sought, using measurements of the anisotropy of magnetic susceptibility. The observed magnetic grain alignment indicates that the flow was essentially uniform and horizontal across the hexagons which were sampled. The flow probably occurred during emplacement of the lava; there is no evidence of convection within the hexagons, either from the degree of grain alignment or its orientation.