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1.
To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P c and cumulative fraction V c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V c and relaxation time T 2 show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.  相似文献   

2.
Two-dimensional Hurst Index of Joint Surfaces   总被引：2，自引：1，他引：2  
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3.
Summary Many rock mass classification systems exist to assist the engineer in assessing the rock support requirements for underground design. On-going research in this area is directed at attempting to utilize the fractal dimension and the acoustic emission response of the tuffs at the Nevada Yucca Mountain to further aid in rock mass classification. Acoustic emission response is shown to be correlated with the porosity of the sample. Engineering behaviour of the rock varies dramatically with porosity; events and peak amplitude offer a means to distinguish between fracture porosity and pore porosity and consequently the engineering behaviour of the rock. Fractal dimension is used to characterize the roughness of fracture surfaces. Two fractal dimension calculation methods, one based on the semi-variogram for the surface and the other based on the use of dividers, are applied for this purpose. The divider method is shown to resolve deviation from a straight line; the semi-variogram method is shown to identify statistical similarity to various types of noise.Nomenclature D fractal dimension - AE acoustic emission - b b-value determined from log(frequency) against log(amplitude) plots - (h) semi-variogram function - h lag distance for semi-variogram function - H an exponent term related to fractal dimension asD=2 –H  相似文献   

4.
The aim of the presented study is to assess the fractal dimension (D) and the geometrical characteristics (length and width) of the landslides identified in North of Tehran, Iran. At first, the landslide locations (528 landslides) were identified by interpretation of aerial photographs, satellite images and field surveys, and then to calculate the fractal dimension (D), we used the computer programming named as FRACEK. In the next step, geometrical characteristics of each landslide such as length (L) and width (W) were calculated by ArcGIS software. The landslide polygons were digitized from the mentioned landslide inventory map and rotated based on movement direction. The fractal dimension for all landslides varied between 1.665 and 1.968. Subsequently, the relationship between the length/width ratios and theirs fractal D values for 528 landslides was calculated. The results showed that correlation coefficients (R), which are different regression models such as exponential, linear, logarithmic, polynomial, and power, between D and L/W ratio are relatively high, respectively (0.75, 0.75, 0.76, 0.78, and 0.75). It can be concluded that the fractal dimension values and geometry characteristics of landslides would be useful indices for the management of hazardous areas, susceptible slopes, land use planning, and landslide hazard mitigation.  相似文献   

5.
The ongoing continent?Ccontinent collision between Indian and Eurasian plates houses a seismic gap in the geologically complex and tectonically active central Himalaya. The seismic gap is characterized by unevenly distributed seismicity. The highly complex geology with equally intricate structural elements of Himalaya offers an almost insurmountable challenge to estimating seismogenic hazard using conventional methods of Physics. Here, we apply integrated unconventional hazard mapping approach of the fractal analysis for the past earthquakes and the box counting fractal dimension of structural elements in order to understand the seismogenesis of the region properly. The study area extends from latitude 28°N?C33°N and longitude 76°E?C81°E has been divided into twenty-five blocks, and the capacity fractal dimension (D 0) of each block has been calculated using the fractal box counting technique. The study of entire blocks reveal that four blocks are having very low value of D 0 (0.536, 0.550, 0.619 and 0.678). Among these four blocks two are characterized by intense clustering of earthquakes indicated by low value of correlation fractal dimension (D c ) (0.245, 0.836 and 0.946). Further, these two blocks are categorized as highly stressed zones and the remaining two are characterized by intense clustering of structural elements in the study area. Based on the above observations, integrated analysis of the D c of earthquakes and D 0 of structural elements has led to the identification of diagnostic seismic hazard pattern for the four blocks.  相似文献   

6.
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D f) of the whole MSN computed through box-counting method.  相似文献   

7.
Natural rock joint roughness quantification through fractal techniques   总被引：8，自引：0，他引：8  
Accurate quantification of roughness is important in modeling hydro-mechanical behavior of rock joints. A highly refined variogram technique was used to investigate possible existence of anisotropy in natural rock joint roughness. Investigated natural rock joints showed randomly varying roughness anisotropy with the direction. A scale dependant fractal parameter, K v, seems to play a prominent role than the fractal dimension, D r1d, with respect to quantification of roughness of natural rock joints. Because the roughness varies randomly, it is impossible to predict the roughness variation of rock joint surfaces from measurements made in only two perpendicular directions on a particular sample. The parameter D r1d × K v seems to capture the overall roughness characteristics of natural rock joints well. The one-dimensional modified divider technique was extended to two dimensions to quantify the two-dimensional roughness of rock joints. The developed technique was validated by applying to a generated fractional Brownian surface with fractal dimension equal to 2.5. It was found that the calculated fractal parameters quantify the rock joint roughness well. A new technique is introduced to study the effect of scale on two-dimensional roughness variability and anisotropy. The roughness anisotropy and variability reduced with increasing scale.  相似文献   

8.
Summary A new concept of feature size range of a roughness profile is introduced in the paper. It is shown that this feature size range plays an important role in estimating the fractal dimension,D, accurately using the divider method. Discussions are given to indicate the difficulty of using both the divider and the box methods in estimatingD accurately for self-affine profiles. The line scaling method's capability in quantifying roughness of natural rock joint profiles, which may be self-affine, is explored. Fractional Brownian profiles (self-affine profiles) with and without global trends were generated using known values ofD, input standard deviation, , and global trend angles. For different values of the input parameter of the line scaling method (step sizea 0),D and another associated fractal parameterC were calculated for the aforementioned profiles. Suitable ranges fora 0 were estimated to obtain computedD within ±10% of theD used for the generation. Minimum and maximum feature sizes of the profiles were defined and calculated. The feature size range was found to increase with increasingD and , in addition to being dependent on the total horizontal length of the profile and the total number of data points in the profile. The suitable range fora 0 was found to depend on bothD and , and then, in turn, on the feature size range, indicating the importance of calculating feature size range for roughness profiles to obtain accurate estimates for the fractal parameters. Procedures are given to estimate the suitablea 0 range for a given natural rock joint profile to use with the line scaling method in estimating fractal parameters within ±10% error. Results indicate the importance of removal of global trends of roughness profiles to obtain accurate estimates for the fractal parameters. The parametersC andD are recommended to use with the line scaling method in quantifying stationary roughness. In addition, one or more parameters should be used to quantify the non-stationary part of roughness, if it exists. The estimatedC was found to depend on bothD and and seems to have potential to capture the scale effect of roughness profiles.  相似文献   

9.
《Engineering Geology》2002,63(1-2):141-155
Fractal theory is used in the present study to develop a more reliable method for rock mass characterization. Field studies have been carried out in opencast mines of dolomite, limestone, fluorite; sandstone and shale in coalmines. Fractal dimension of blasted fragments (Dfrag) and in situ rock blocks (Din situ) is calculated using size distribution curves according to Schumann's model. Based on the co-relation between Uniaxial Compressive Strength (UCS) and Dfrag, it is observed that change in fractal dimension is nominal beyond the UCS value of 20. From the co-relation between Bieniawaski's Rock Mass Rating (RMR) and Din situ, it is found that there is a sharp increase in fractal dimension for RMR greater than 40. Co-relation between RMR and Dfrag/Din situ shows that as RMR increases, Dfrag/Din situ ratio decreases. Rock mass classification based on fractal geometry is suggested.  相似文献   

10.
Quantification of Natural Fracture Surfaces Using Fractal Geometry   总被引：3，自引：0，他引：3  
The purpose of this paper is to present an extensive evaluation of the methods to calculate the fractal dimension of natural fracture surfaces. Three methods; variogram analysis (VA), power spectral density (PSD), and roughness-length method (RMS) are applied to 2-D surface data (PSD) and 1-D profiles (VA and RMS) extracted from the surface data of 54 mm diameter crystallized limestone samples. Surface topography of the samples is quantified through a newly designed fully automated device. Before the application, self-affinity of the surface roughness and the applicability of these methods are validated using synthetically generated fractal surfaces. Fractal dimension values of the profiles are obtained as between 1 and 1.5 with a few exceptions. VA and RMS methods yield consistent fractal dimensions while the PSD values are lower than those of the other two methods. In terms of practical applicability, the VA is found more convenient than other two methods because there still exists shortcomings with the PSD and RMS methods due to difficulties in the mathematical analysis of the plots whose slopes are used in the computation of fractal dimension. However, it is observed that the data of limited size fracture surfaces are convenient for fractal analysis and the results are promising for further applications if the fracture surface size is restricted like cores recovered from deep boreholes.  相似文献   

11.
黑龙江省逊克县高松山金矿床地质分形特征及成矿预测   总被引：1，自引：0，他引：1  
高松山金矿床是中国人民武装警察部队黄金第一支队在小兴安岭-张广才岭成矿带北段发现的大型浅成低温热液矿床,随着研究的深入,发现其具有优越的成矿地质条件和良好的找矿前景。在总结前人成果的基础上,文章利用分形学理论对金矿资源量和品位进行了分析,结果显示资源量在大于250 kg标度区间时,分维数D值为1.69,表明资源量在该区段内的普查存在较好的前景,同时,品位分维数D值为1.10~1.40时,其成矿仅与细脉状烟灰色石英-细粒黄铁矿成矿阶段紧密相关。利用钻孔资料分析品位在垂向上的分形特征发现,分维数D值介于1~1.5时,表现为垂向不圈闭延伸,反映其深部可能存在隐伏矿体。在资源评价方面,通过对断裂构造似等距控矿规律的研究,结合帕累托定律（Pareto law）和阻尼曲线模型,对深部可能存在的矿体规模和部位进行了预测,资源量大于4960 kg的矿体仍有2处未发现,中等资源量规模的矿体存在巨大空间,同时,预测隐伏矿体可能在已有地表矿体相间部位的深部。  相似文献   

12.
Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation.  相似文献   

13.
Himalayan seismicity is related to continuing northward convergence of Indian plate against Eurasian plate. Earthquakes in this region are mainly caused due to release of elastic strain energy. The Himalayan region can be attributed to highly complex geodynamic process and therefore is best suited for multifractal seismicity analysis. Fractal analysis of earthquakes (mb ?? 3.5) occurred during 1973?C2008 led to the detection of a clustering pattern in the narrow time span. This clustering was identified in three windows of 50 events each having low spatial correlation fractal dimension (D C ) value 0.836, 0.946 and 0.285 which were mainly during the span of 1998 to 2005. This clustering may be considered as an indication of a highly stressed region. The Guttenberg Richter b-value was determined for the same subsets considered for the D C estimation. Based on the fractal clustering pattern of events, we conclude that the clustered events are indicative of a highly stressed region of weak zone from where the rupture propagation eventually may nucleate as a strong earthquake. Multifractal analysis gave some understanding of the heterogeneity of fractal structure of the seismicity and existence of complex interconnected structure of the Himalayan thrust systems. The present analysis indicates an impending strong earthquake, which might help in better hazard mitigation for the Kumaun Himalaya and its surrounding region.  相似文献   

14.
Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r B andr L ) asD=log (r B )/log (r L ). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr B andr L are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins.  相似文献   

15.
Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K v, plays a more prominent role than the fractal dimension, D a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D a1d and K v, D a1d × K v, is suggested to capture the aperture anisotropy.  相似文献   

16.
The spatial distribution of joint orientations features self-similarity. Based on the fractal theory, a new method for meshing of Schmidt pole diagram has been established to study the fractal dimension of the orientation pole distribution of joint. Meshing of Schmidt pole diagram by equal area is performed in both circumferential and radial directions. When the cycle number n is set, the circle is evenly divided with n diameter lines to obtain 2n sectors of equal area; meanwhile the radius R is divided n times to obtain n rings, and specific ring radii are set to perform meshing of Schmidt pole diagram by equal area, thus obtaining different side lengths of cells and corresponding number of cells occupied by poles; on this basis the fractal dimension of joints was calculated. This method is applied to the research on the fractal dimension of joints in rock mass of mine. The results of the research showed that the method with fewer parameters made the process in which the fractal dimension of the orientation pole distribution of joint was solved simply and easy to operate, and calculating the fractal dimension of the orientation pole distribution for joint by this method could better describe the dispersity and complexity of the orientation distribution of joint.  相似文献   

17.
岩石节理粗糙度系数的分形特征   总被引：5，自引：0，他引：5  
岩石节理粗糙度系数JRC是估算节理抗剪强度和变形指标最重要的参数。通过对简易纵剖面仪获取的节理表面轮廓曲线的分形研究,讨论了节理表面轮廓曲线的自相似性和JRC的自相似性,并根据实测统计资料的分析,指出了分形理论研究JRC的适用条件和有效的使用方法。由实测统计资料的JRC尺寸效应自相似性分析,认为JRC尺寸效应具分形结构。本文介绍了一种确定JRC尺寸效应分维数D的方法,由此确定的分维数D具有明确的物理意义。  相似文献   

18.
Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod.  相似文献   

19.
High-velocity friction experiments on gabbro and monzodiorite, using a rotary-shear high-velocity friction apparatus, have revealed that frictional melting and progressive growth of a molten layer along a fault cause slip weakening, eventually reaching a nearly steady-state. The melting surface at the host rock/molten layer interface is initially very flat, but it becomes more complex and rounded in shape towards the steady state owing to the selective melting of minerals with lower melting points and the Gibbs–Thomson effect. This change in the melting-surface topography can be quantitatively expressed by the fractal dimension D, as determined by the divider method, from about 1.0 near the peak friction to around 1.1 near the steady-state friction. The ultimate fractal dimension at steady-state friction tends to decrease with increasing heat production rate presumably due to more rapid and uniform melting. A systematic correlation of D with mechanical behavior of the fault during frictional melting may provide a way of estimating slip-weakening distance and heat production rate at steady-state friction by measuring D for natural pseudotachylytes on slip surfaces with different displacements. The weakening distance is of vital significance in relation to fault instability and the heat production rate is related to the fault strength. The experimental studies point to ways to estimate these difficult quantities for natural faults.  相似文献   

20.
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D f) of the whole MSN computed through box-counting method.  相似文献   

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