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1.
文中以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,通过野外裂隙调查,应用传统的概率统计方法与分形几何学理论,利用Mapinfo,ArcGIS平台进行裂隙几何学参数(方位、长度、密度等)的统计、计算和裂隙网络的空间结构分析,研究花岗岩岩体中裂隙的几何学特征。并以此为基础,对甘肃北山花岗岩岩体质量优劣进行初步评价。结果表明:在10～200cm范围内,裂隙网络是分形的;5个测点裂隙网络的分维值分别是1.636,1.548,1.596,1.724,1.604。分维数D不仅能刻画岩体中结构面发育的数量,而且能反映结构面在岩体中分布的均匀程度和交切方式。因此,可以表征岩体的质量优劣,对岩体质量进行分级。按照分维所划分的岩体质量分级,北山花岗岩属于裂隙较发育、岩体质量等级一般的岩体 相似文献
2.
Influences of Aquifer Properties on Flow Dimensions in Dolomites 总被引：1，自引：0，他引：1
by Timotej Verbov&#;ek 《Ground water》2009,47(5):660-668
The paper focuses on analyses and correlations of flow dimensions in different dolomite aquifers in Slovenia. Flow dimensions are obtained through the reinterpretation of 72 pumping tests with the generalized radial flow model, based on the fractional flow dimension. The average value of flow dimensions is 2.16 for all dolomites. A study of flow dimensions in individual aquifers categorized according to their lithological properties shows that higher dimensions occur in massive late-diagenetic Cordevolian and Anisian dolomites compared with bedded Main, Bača, and especially Lower Triassic dolomites, which contain a greater proportion of noncarbonate minerals. Partially penetrating wells have higher flow dimensions than fully penetrating wells. Flow dimensions are poorly correlated with hydraulic conductivities of fractures. When comparing the quantities of major dissolved minerals, obtained by hydrogeochemical inverse modeling, with the values of flow dimensions, the Cordevolian and Anisian dolomites are found to exhibit the highest values of both dissolved dolomite and flow dimensions, indicating that greater dissolution occurs at higher flow dimensions. For other aquifers, data points are more scattered and the correlation is mostly poor. When compared with three-dimensional fractal dimensions of fracture networks, there is no correlation with flow dimensions. However, almost all the values of flow dimensions are lower than the corresponding fractal dimensions in dolomites (average D = 2.77), possibly indicating the channeling of flow within the available space of the fracture networks, consequently reducing the flow dimensions. 相似文献
3.
We present a case of detailed analysis of fracture arrays spanning four orders of magnitude in length; all of them measured at a single natural site by acquiring images at progressively larger scales. There is a high dispersion of cumulative-length exponents, box dimensions and fracture densities. However, the fractal analysis supports the fractal nature of fracture arrays. Our data indicate the existence of an upper limit for the density parameters, as similarly reported by other authors. We prove that box dimension is in inverse relation with fracture concentration and in direct relation with fracture density. These relations are also observed in our data and additionally there is an upper limit for the box dimensions. We interpret the dispersion in our results as more fundamental than methodological problems. It represents a truncation in the complete evolution of the fracture systems because in natural cases strain initiates overprinting of previous fracture arrays. Considering that larger fractures accommodate strain more efficiently than small fractures, the generation of small fractures is inhibited in the presence of pre-existing larger fractures. Maximum values of fracture density prevent accommodating an excess of strain in a single or restricted range of scales; we claim this condition produces migration of fracturing to larger scales originating fracture scaling. 相似文献
4.
The fractal geometry of flow paths in natural fractures in rock and the approach to percolation 总被引：2，自引：0，他引：2
The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold. 相似文献
5.
Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets 总被引：1，自引：0，他引：1
—Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension.¶Mutual relations between the three most popular fractal dimensions, namely the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal dimensions on epicenter distribution, and relations among the fractal dimensions, are complex and variable. Neither values nor even inequalities among dimension estimates are preserved when different fractal dimensions are used. The correlation and the capacity dimensions seem to be good tools to trace collinear tendencies of eipicenters while the cluster dimension is more appropriate to studying uniform clustering of points. 相似文献
6.
本文研究了岩石分形断裂的统计理论.认为岩石断裂是岩石内部微裂缝成核、形成和传播的非平衡过程,导出了描述这个过程的微分方程.运用位错塞积成核机理,得到了岩石发生分形断裂的微裂缝大小的统计分布函数和平均长大速率.从理论上得出了岩石非弹性体积应变与微裂缝数目成正比,从而解释了实验室研究的结果.另外发现岩石的分维是决定岩石脆性的一个重要因素,分维值愈小,岩石愈脆.但岩石的分维值与岩石强度无明显关系.最后,从微裂缝大小的统计分布函数出发,导出了b值与岩石分维值的关系. 相似文献
7.
采用关联维方法对台湾地区地震活动的空间特征进行了研究。先利用 10 0a来台湾的地震目录计算各个地震区、带的关联维数 ,将地震空间分布的分形特征定量表达出来 ,然后综合分析地震空间分布的关联维数和孕震构造环境之间的关系 ,得出了以下结论 :1)台湾东、西部地震区由于地震属于不同的大地构造单元 ,因此关联维数有较大的差异 ;2 )在各地震区内部的各个地震带由于板块构造、地壳结构、活断层分布上的差异 ,而具有与其构造特征相对应的关联维数 ;3)各地震带内部的各个不同的部位又由于不同的构造应力场 ,而导致地震分布上出现不同的丛集性 ,表现为不同的关联维数。这些结论充分说明通过关联维分析所得到的地震活动的空间图像与地震活动所代表的不同地质构造背景有着良好的对应关系 相似文献
8.
9.
Shi Xingjue Xu Heming Niu Zhiren Fan ZengjieUniversity of Science Technology of China Hefei China Seismologicai Bureau of Shanxi Xi'an China 《中国地震研究》1994,(3)
The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same res 相似文献
10.
Fractal generation of surface area of porous media 总被引：2，自引：0，他引：2
Hongbing Sun Manfred Koch 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(2):83-96
Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they
are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify
a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure
with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating
a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is
presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic
porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a
nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which
is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity,
the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical
fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation
structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean,
variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately
2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous
medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82.
The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy
assumed. 相似文献
11.
Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they
are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify
a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure
with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating
a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is
presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic
porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a
nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which
is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity,
the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical
fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation
structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean,
variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately
2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous
medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82.
The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy
assumed. 相似文献
12.
13.
Noelle E. Odling 《Pure and Applied Geophysics》1992,138(1):95-114
The influence that fractures exert on the permeability of a fractured rock is, to a large extent, controlled by the nature of the network formed by the fracture system. Here, the network properties of a two-dimensional natural pattern, mapped from the surface of a sandstone layer, are investigated and compared to those of realizations of spatially randomly distributed line segments with similar orientation and length distributions and line segment density (line length per unit area) to the natural pattern. These patterns are composed of clusters of varying size and shape, made up of interconnected fracture traces or line segments. Comparing the natural pattern with the realizations, the natural pattern was found to contain roughly half the number of clusters while the mass (total line length) of the largest cluster is approximately double that of the realizations. The size of the largest cluster controls the connectivity of the patterns, as can be seen by comparing the largest cluster of the natural pattern, which connects all four sides of the region, with those of the realizations, which are unconnected or connect only two sides. Cluster scaling characteristics were found to be similar in the natural pattern and the realizations and show a crossover from a dimension of one (their topological dimension) to two (the dimension of the embedding medium) at a point that corresponds to the fracture spacing. An investigation of the self-similarity dimension, using the box-counting method, showed similar characteristics with a broad transition zone between one- and two-dimensional behaviour at smaller box sizes. The patterns are therefore found to be non-fractal. The effect of the spatial distribution shown by the natural pattern is thus to modify the manner in which fractures are distributed among clusters, increasing connectivity (and permeability in the case of open fractures), but does not affect the cluster scaling characteristics or the self-similarity dimension of the fracture patterns. 相似文献
14.
Jérôme Weiss 《Surveys in Geophysics》2003,24(2):185-227
The scaling properties of fracture and faulting of ice on Earth are reviewed.Numerous evidences for the scaling of fracture and faulting of ice are given,including self-affine fracture surfaces, fractal fracture networks at small(laboratory) and large (geophysical) scales, power law distributions of fracturelengths or of fragment sizes within fault gouges. These scaling laws are discussedin terms of the underlying mechanics. Scaling of the observables associated withfracture and faulting argues for the scale invariance of the fracture and faultingprocesses and indicates that small scales cannot be arbitrarily disconnected fromlarge scales. Consequently, quantitative links between scales cannot be performedthrough classical homogenization procedures. Scaling can also induce scale effectson different mechanical parameters such as fracture energy, strength or stiffness.Although scaling is ubiquitous for the fracture of ice on Earth, important exceptionsexist such as the nucleation of microcracks or the crevassing of glaciers. Theseexceptions are stressed and discussed. 相似文献
15.
I. Lerche 《Pure and Applied Geophysics》1993,140(3):503-517
In order to assess the degree of uncertainty of fractal dimensionality, a procedure is given which provides a cumulative probability measure of uncertainty of fractal dimensionality in terms of assessments of range and most likely value. The procedure allows for a variation of the model proposed (i.e., variability of the parameters involved in the fractal relation) and leads to a relevant estimate of the uncertainty. The procedure is simple to apply and useful in providing a statistically valid comparison of results.As an illustration, the procedure was used on the fractal dimensions of faults measured from shear zones of different scale magnitudes. Results suggest that these shear zones are indeed quantitatively similar with a fractal dimension around 1.5. It is also shown that the range of uncertainty of the fractal dimensionality (90% likelihood range) is sensitive to the amount of data used to calculate the fractal dimension of the faults. 相似文献
16.
断层岩的粒度分布包含岩石破裂机制、摩擦性质和地震能量分配等重要信息。筛分-称重和激光测量是分析断层岩三维粒度的2种有效方法,但每一种方法的测量范围仅有3个量级,难以全面反映断层岩的粒度分布特征。利用上述2种方法对汶川地震断层滑动带上的断层岩（简称断层岩）的粒度分布进行了测量,粒径测量范围从0.2μm至16mm,跨度达到5个数量级。结果显示：1）存在临界粒径dc（0.95～1.90μm）。粒度大于和小于dc的颗粒满足不同的颗粒数（Nd）-粒径（d）分布关系,表明该断层岩的粒径分布不具有自相似性特征。2）利用粒度大于dc的颗粒计算出的分形维数与断层岩类型有很好的相关性,即断层带边缘的角砾岩的平均分形维数为2.6,核部压碎角砾岩的平均分形维数约为3.0,中心断层泥的分形维数约为3.5。粒径小于dc的颗粒的分形维数为1.7～2.1。分形维数的突变反映出断层破裂机制的复杂性,即在不同的粒度域,岩石的破裂机制不尽相同。3）依据粒度分析结果,估算出汶川地震断层泥的单位破裂能（Es）为0.63MJ/m2。 相似文献
17.
本文就地震预报中常用的分形几何中的几个数学概念做了简要的介绍，包括测度，豪斯道夫维数、计盒维数等，并介绍了有关维数的性质和估计方法。作者试图通过了这些数学概念的简要介绍，使读者对分维有更准确的理解。 相似文献
18.
Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales 总被引：18，自引：0，他引：18
Takayuki Hirata 《Pure and Applied Geophysics》1989,131(1-2):157-170
Based on fault maps, whether or not the fracture geometry of rocks is self-similar, was examined by using a box-counting algorithm. The statistical self-similarity (fractal structure) of the fault fracture systems holds well at the scale of about 2 to 20 km. The fractal dimension in Japan varied from 1.05 to 1.60. The fractal dimension is about 1.5–1.6 at the central part of the Japan Arc, and decreases with distance from the center. At a smaller scale, the fractal structure also holds well in the rock fracture geometry. The fractal dimension of the North Izu Peninsula fault system (branching faults) is 1.49 at the scale of 0.625 to 10 km, the fractal dimension of rock fracture geometry at the scale order of 10–1 to 10–2 meters is about 1.49–1.61. The upper limit of the fractal dimension of rock fracture geometry is about 1.6, judging from the estimation of fractal dimension on actual fracture geometry of rocks. This value may impose a restraint on modeling of faulting and the fracture process of rocks. 相似文献
19.
Fractal analysis of long-range paleoclimatic data: Oxygen isotope record of pacific core V28-239 总被引：1，自引：0，他引：1
R/S analysis of the oxygen isotope curve of Pacific core V28-239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing O18 ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 106 years. Given this temperature curves based on fractal parameters of long-term O18 data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible. 相似文献
20.
Shifang Wang Boming Yu Qian ZhengYonggang Duan Quantang Fang 《Advances in water resources》2011,34(12):1574-1580
An analytical expression is derived for the starting pressure gradient for Bingham fluids in porous media embedded with randomly distributed fractal-like tree networks based on fractal theory and technique. The proposed model relates the flow rate and the starting pressure gradient to the structural parameters of porous media and microstructural parameters of fractal-like tree networks, the yield stress and fractal dimensions of porous media and maximum mother diameter of randomly distributed fractal-like tree networks. The results show that the starting pressure gradient decreases with the increase of porosity of matrix material, fractal dimension for mother diameters, diameter ratio and permeability, and the starting pressure gradient increases with the increase of the length ratio and the yield stress. The model predictions from the present model for the starting pressure gradient are in good agreement with the available expression. 相似文献