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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.
The basic quality (BQ) system is regarded as the national rock mass classification system that can be appropriate for use in most types of rock engineering in China. Two underlying parameters that the uniaxial compressive strength (UCS) and the rock intactness index (KV) are taken into account to access the basic BQ value. However, The KV was usually measured by an indirect acoustic wave approach which often cannot reflected the actual conditions. In this study, a direct measured parameter KGSI is recommended to obtain by means of the GSI system to replace the original KV, and a new method [BQ]GSI expressed by the new parameter KGSI is proposed. In particular, a graphic method is also presented to determine rapidly and rationally the rock mass classification by the X, Y coordinates of the UCS and the KGSI. In order to further compare the evaluation results and application effects between the [BQ]GSI and the international rock mass classification systems, a comprehensive solution is carried out. First, the evaluation factors of rock mass qualities from all these system are classified according to three groups: the rock mass inherent parameters, external parameters, and construction parameters. Second, the correlations among these evaluation factors in the new [BQ]GSI system and the common international systems (i.e. RMR, Q, and RMi) were compared. And the formulas or charts among the three groups are presented. Finally, five hydropower underground excavations are chosen to analysis the comparison results of the [BQ]GSI system and the international common RMR, Q, or RMi systems. The applicability scope of these international RMR, Q, or RMi systems is also discussed in the context of China’s rock characteristics and geological stress conditions.  相似文献   

3.
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   

4.
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   

5.
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   

6.
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   

7.
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   

8.
Geotechnical investigation projects in Korea produced data on the in situ modulus of deformation of rock masses (E M) measured with the borehole test, rock mass rating (RMR), and Q-system. The modulus of deformation of rock masses was correlated with the degree of weathering, RMR, and Q values. Determination of E M for each degree of weathering allows for the results to be used to classify the degree of weathering or to predict E M. The relation between E M and RMR is represented by $ E_{\text{M}} = 10^{{\frac{{{\text{RMR}} - 16}}{50}}} $ , which returns values 2–3 times lower than those reported in previous studies. Despite scatter in the values, due to larger dataset used in this study, the proposed equation may be used to predict the in situ modulus of deformation from RMR values. In addition, the relation between modulus of deformation and Q values is $ E_{\text{M}} = 10^{{0.32{ \log }Q + 0.585}} $ .  相似文献   

9.
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   

10.
The experimental determination of anelastic strain recovery (ASR) compliances for three types of rocks (granite, marble, and sandstone) was performed in the laboratory. Preloading of specimens for uniaxial compression creep tests was at 50 % of the uniaxial compressive strength (UCS) for each rock type. We obtained the shear mode Jas(t) and volumetric mode Jav(t) ASR compliances and calculated the ratio of Jas(t) to Jav(t). The Kelvin model for rock rheology was then applied in numerical simulations and the results were in good agreement with the measured data for Jas(t) and Jav(t). These results showed that both the magnitude and rate of increase of the ASR compliances are strongly dependent on the rock type, and the values of the Jas(t)/Jav(t) ratio for a loading of 50 % of the UCS showed a trend leading to different constants for each of the three rock types. Further experimental and numerical analyses showed approximate power-law relationships between the ASR compliances at 50 % of UCS, and both the UCS and the tangential Young’s modulus at 50 % of UCS (E t50). These relationships may be useful for the preliminary estimation of ASR compliances.  相似文献   

11.
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   

12.
For several decades, sedimentologists have had difficulty in obtaining an efficient index of particle form that can be used to specify adequately irregular morphology of sedimentary particles. Mandelbrot has suggested the use of the fractal dimension as a single value estimate of form, in order to characterize morphologically closed loops of an irregular nature. The concept of fractal dimension derives from Richardson's unpublished suggestion that a stable linear relationship appears when the logarithm of the perimeter estimate of an irregular outline is plotted against the logarithm of the unit of measurement (step length). Decreases in step length result in an increase in perimeter by a constant weight (b) for particles whose morphological variations are the same at all measurement scales (self-similarity). The fractal dimension (D) equals 1.0-(b), where b is the slope coefficient of the best-fitting linear regression of the plot. The value of D lies between 1.0 and 2.0, with increasing values of D correlating with increasing irregularity of the outline. In practice, particle outline morphology is not always self-similar, such that two or possibly more fractal elements can occur for many outlines. Two fractal elements reflect the morphological difference between micro-scale edge textural effects (D1) and macro-scale particle structural effects (D2) generated by the presence of crenellate-edge morphology (re-entrants). Fractal calibration on a range of regular/irregular particle outline morphologies, plus examination of carbonate beach, pyroclastic and weathered quartz particles indicates that this type of analysis is best suited for morphological characterization of irregular and crenellate particles. In this respect, fractal analysis appears as the complementary analytical technique to harmonic form analysis in order to achieve an adequate specification of all types of particles on a continuum of irregular to regular morphology.  相似文献   

13.
A Fractal Description of Simulated 3D Discontinuity Networks   总被引：1，自引：1，他引：0  
  相似文献   

14.
In the present study, the grain size (d) and shape of 225 magnetite grains, that crystallized at T>600°C in a syntectonic granite (Godhra Granite, India) are evaluated and implications of data to decipher deformation mechanism of magnetite are discussed. Fractal (ruler) dimension (D) analysis of magnetite grains is performed and it is demonstrated that they show fractal behaviour. Smaller magnetite grains tend to be more serrated than the larger ones, which is manifested in the higher fractal (ruler) dimension (D) of the former. Assuming a natural strain rate ranging between 10−10 s−1 and 10−14 s−1, the grain size data fall dominantly in the dislocation creep field of the existing deformation mechanism map of magnetite for 630°C. However, SEM-EBSD studies reveal that subgrains are absent in the magnetite grains and they did not undergo dislocation creep. Thus it is inferred that the shape of magnetite grains was not controlled by dislocation creep. It is concluded that the higher serration and increased fractal dimension of finer magnetite grains implies the importance of diffusion creep as an important deformation mechanism at high-T for magnetite in polymineralic rocks.  相似文献   

15.
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   

16.
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   

17.
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   

18.
At this paper, we studied about the rock quality of Shirinrud dam site by engineering seismology. Shirinrud dam site is located 80 km far from Kerman and 18 km far from Hojadk village. The dam and its constructions are established in the Bidu Formation which consists of seven rock units, and the refraction profiles were surveyed on Jb3/2, Jb4, and Jb5 rock units. To evaluate the rock mass quality and basement topography at this site, nine refraction seismic profiles by primary waves and two refraction seismic profiles by secondary waves were surveyed. We used some methods such as Palmer method, the reciprocal method, plus–minus method, etc. to process and interpret data. Based on investigations, primary wave velocity in unit Jb3/2 varies between 2,100 and 2,200 m/s, in unit Jb4 is between 2,100 and 4,200 m/s, and in unit Jb5 is between 2,500 and 3,000 m/s. The Q values on these three units are 0.05, 1.2, and 1.9, and the rock mass rating (RMR) values are 27.1, 40.5, and 33.5, respectively. With respect to wave velocity, Q, and RMR values, the units Jb3/2, Jb4, and Jb5 are evaluated as very weak, intermediate, and weak, respectively.  相似文献   

19.
Changes in the hydraulic conductivity field, resulting from the redistribution of stresses in fractured rock masses, are difficult to characterize due to complex nature of the coupled hydromechanical processes. A methodology is developed to predict the distributed hydraulic conductivity field based on the original undisturbed parameters of hydraulic conductivity, Rock Mass Rating (RMR), Rock Quality Designation (RQD), and additionally the induced strains. The most obvious advantage of the methodology is that these required parameters are minimal and are readily available in practice. The incorporation of RMR and RQD, both of which have been applied to design in rock engineering for decades, enables the stress-dependent hydraulic conductivity field to be represented for a whole spectrum of rock masses. Knowledge of the RQD, together with the original hydraulic conductivity, is applied to determine the effective porosity for the fractured media. When RQD approaches zero, the rock mass is highly fractured, and fracture permeability will be relatively high. When RQD approaches 100, the degree of fracturing is minimal, and secondary porosity and secondary permeability will be low. These values bound the possible ranges in hydraulic behaviour of the secondary porosity within the system. RMR may also be applied to determine the scale effect of elastic modulus. As RMR approaches 100, the ‘softening’ effect of fractures is a minimum and results in the smallest strain-induced change in the hydraulic conductivity because the induced strain is uniformly distributed between fractures and matrix. When RMR approaches zero, the laboratory modulus must be reduced significantly in order to represent the rock mass. This results in the largest possible change in the hydraulic conductivity because the induced strain is applied entirely to the fracture system. These values of RMR bound the possible ranges in mechanical behaviour of the system. The mechanical system is coupled with the hydraulic system by two empirical parameters, RQD and RMR. The methodology has been applied to a circular underground excavation and to qualitatively explain the in situ experimental results of the macropermeability test in the drift at Stripa. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

20.
In this study, an assessment of seismicity parameters in the northwest Himalaya and adjoining regions using an earthquake catalog from India Meteorological Department covering a period from June 1, 1998 to June 30, 2011 has been carried out. The spatial distributions of seismicity parameters, namely magnitude of completeness, M C, a value, b value, and correlation fractal dimension, D C, are estimated for the studied region. The M C, a, and b values are found to be 2.5, 4.601, and 0.83, respectively. Despite significant gaps, the spatial distributions of a and b values are seen to follow similar trend and are found scattering in between Main Boundary Thrust (MBT) and South Tibet Detachment, adjoining areas of Mahendragarh-Dehradun Fault (MDF), Delhi-Haridwar Ridge (DHR) and Moradabad Fault (MF), and the southern flank of Karakoram Fault and Indus-Tsangpo Suture Zone. The estimated spatial distribution of b and a values is within 90 % of confidence level, thereby indicating non-uniform stress accumulation or higher rock fracturing density in the studied region caused by strong tectonization following several earthquakes. Negative correlation between low b value and high D C is observed predominantly in the region between the MBT and Munsiari Thrust or Main Central Thrust-I of Garhwal and Kumaon Himalaya, adjoining zones of MDF, DHR, and MF of Indo-Gangetic plain, and the eastern flank of the studied region, suggesting the presence of asperities in the zone. At the same time, active creeping process can be inferred in between the MBT and Main Central Thrust of Garhwal Himalaya and the surrounding areas of Shimla region of the Himalayan arc to the northwestern part of the studied region from the positive correlation between b value and D C. The results indicate that the structural heterogeneity caused by different stress accumulation and rock fracturing densities exists due to continuous tectonic adjustments between different geomorphic features of the studied region. An attempt has also been made to classify the studied region into smaller seismic zones by observing the spatial patterns of b value and D C that are fractal properties of the observed seismicity, along with the prevalent fault networks.  相似文献   

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