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1.
The observed fractal nature of both fault length distributions and earthquake magnitude-frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity. In previous theoretical work, a positive correlation between the exponent D from the fracture length distribution, and the seismic or acoustic emission (AE) b-value has been inferred from a simple dislocation model of the seismic source. Here, we present the first experimental evidence for a correlation between D and b from a series of tensile fracture mechanics tests on crystalline rock, carried out in different environmental conditions, both air-dry and water-saturated, and at ambient temperature and pressure. The microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity, KI, and quantitative analyses of the resulting fracture patterns were carried out on the same specimens. It is found that AE b-values, ranging from 1.0 to 2.3, correlate negatively with the normalized stress intensity KI/KIC, where KIC is the fracture toughness of the specimen. The microcrack length distribution exponent D, ranges from 1.0 to 1.7. Fluid presence has a first-order influence on both the AE and structure produced in these experiments. For experiments at low stress intensity or high fluid content, the activation of the stress corrosion mechanism for KI < KIC leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions, reflected in higher values of D and b. The exponent D is found to correlate positively with the AE b-value.  相似文献   

2.
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   

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.
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   

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.
A fractal theory of rock fragmentation is applied to block-and-ash flow deposits from the Fugendake dome, Unzen Volcano, Kyushu, Japan, in order to analyze the material strength and the energy required for size reduction of the source lava dome. Two fractal dimensions h and Ds, which are mutually interchangeable, represent the relative strength and energy for particles reduced to a given size. They can be theoretically estimated from the power relations of a reference grain size to the cumulative mass and number of fragments smaller than that size. The Unzen–Fugendake block-and-ash flow deposits have been further modified by size sorting and secondary fragmentation that occurred during flowage, so that the h value decreases (or Ds value increases) with increasing distance from the source. Coarse, reversely graded deposits are, however, found to retain the original size population relatively well. The Ds values estimated from deposits of this type are compatible with those previously reported from decompression–fragmentation experiments conducted on the same dome material. The employed fractal approach could thus give insights into the potential mode of dome collapse that generates block-and-ash flows.  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.
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   

9.
In this study, the relation between ore grade and geological characteristic has been studied as a principle and also important conceptual in Zarshuran gold deposit in NW Iran. The main subject in this study was identifying a correlation among the ore grade populations and rock types which could be used in other steps of local estimation in the deposit concentration–number (C–N) fractal model and logratio matrix. The C–N log–log plot reveals six geochemical zones defined by Au?<?0.02 ppm as non-mineralized zone and Au?>?0.02 ppm as mineralized zones. According to geological logging and field geology inspection, black gauge, jasperoid, fault gauge and breccia, and carbonaceous rocks are considered as main rock types which contain major Au mineralized zones. The correlation between geological and fractal modeling by logratio matrix shows that there is a good correlation between geological assumed host rocks and C–N fractal modeling. Black gauge rock type with 93.48 % of overall accuracy shows a significant correlation with supergene zone of fractal model, and jasperoid with 92.5 % and carbonaceous rock type with 52.90 % have a decent correlation with highly and lowly mineralized zone of fractal model relatively. Black gauge, jasperoid, and fault gauge and breccia have an approximately near cooperation in this zone for mineralization.  相似文献   

10.
In this study the possibilities of the acoustic emission (AE) technique and deformation rate analysis (DRA) were investigated to measure in situ rock stress. The rock cores were obtained from three vertically drilled exploratory boreholes from the surface and one borehole drilled from within an underground coal mine. The AE method was found to determine in situ rock stress with reasonable accuracy using AE signatures in repeated loadings of a rock core specimen. Based on the results of in situ stress estimation from the AE method, the time interval, up to seven years, did not strongly influence the previous stress determination using the AE method. Cored rock recollected the in situ stress condition reasonably well (within ±10%), when compared to the results from over coring and hydraulic fracturing technique. Also, there was significant correlation between overburden pressure and estimated vertical stress from the AE method.  相似文献   

11.
不同岩石破裂全过程的声发射序列分形特征试验研究   总被引：3，自引：0，他引：3  
吴贤振  刘祥鑫  梁正召  游勋  余敏 《岩土力学》2012,33(12):3561-3569
通过对不同岩性的岩石进行单轴压缩声发射试验,获取岩石破裂全过程中的载荷-轴向变形曲线及声发射参数,观察试件破裂失稳时的破坏情况,分析破坏过程的载荷变化关系。着重对比了不同岩石的不同力学性质、岩石声发射序列的时域特征和声发射序列的分形特征。研究结果表明,采用声发射率、能率可以很好地描述岩石破裂损伤的整个阶段;计算岩石声发射率、声发射能率的关联维数,可得出岩石破裂过程的声发射序列具有分形特征;岩石破裂过程的声发射分维值D反映了岩石内部微裂隙的统计演化规律;不同岩性的岩石破裂过程的声发射参数序列的分形特征具有一定的共性;归纳总结出岩体声发射序列分维曲线的演化模式,即波动→持续下降演化模式,提出可以将分维值的持续下降作为岩体破裂失稳的前兆。  相似文献   

12.
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   

13.
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   

14.
Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.  相似文献   

15.
The Kappa model of probability and higher-order rock sequences   总被引：2，自引：0，他引：2  
In any depositional environment, the sequence of sediments follows specific high- and low-frequency patterns of rock occurrences or events. The occurrence of a rock in a spatial location is conditional to a prior rock event at a distant location. Subsequently, a third rock occurs between the two locations. This third event is conditional to both prior events and is driven by a third-order conditional probability P(C ∣ (A ∩ B)). Such probability has to be characterized beyond the classic conditional independence model, and this research has found that exact computation requires a third-order co-cumulant term. The co-cumulants provide the higher-order redundancy among multiple indicator variables. A Bayesian analysis has been performed with “known” numerical co-cumulants yielding a novel model of conditional probability that is called the “Kappa model.” This model was applied to three-point variables, and the concept has been extended for multiple events P(G ∣ A ∩ B ∩ C ∩ D... ∩ N), allowing the reproduction of complex transitions of rocks in sequence stratigraphy. The Kappa model and co-cumulants have been illustrated with simple numerical examples for clastic rock sequences. In addition, the co-cumulant has been used to discover an extension of the variogram called the indicator cumulogram. In this way, multiple prior events are no longer ignored for evaluating the probability of a posterior event with higher-order co-cumulant considerations.  相似文献   

16.
《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   

17.
Fault-creep events measured on the San Andreas and related faults near Hollister, California, can be described by a rheological model consisting of a spring, power-law dashpotand sliding block connected in series. An empirical creep-event law, derived from many creep-event records analyzed within the constraints of the model, provides a remarkably simple and accurate representation of creep-event behavior. The empirical creep law is expressed by the equation: D(t)= Df [1?1/{ct(n?1)Dfn?1+1}/(n?1)] where D is the value of displacement at time t following the onset of an event, Df is the final equilibrium value of the event displacementand C is a proportionality constant. This discovery should help determine whether the time—displacement character of creep events is controlled by the material properties of fault gouge, or by other parameters.  相似文献   

18.
Laboratory uniaxial tests on cylindrical specimens of a simulated rock are used to identify the influence of the diameter (D) and height (L) of the specimens on the damage parameters. The relations are expressed in terms of the characteristic parameter C = L2/D.  相似文献   

19.
To investigate possible indicators of critical point behavior prior to rock failure, the statistical properties of pre-failure damage were analyzed based on acoustic emission events (AE) recorded during the catastrophic fracture of typical rock samples under differential compression. AEs were monitored using a high-speed 32-channel waveform recording system. Time-dependent statistics, including the energy release rate, b-value of the magnitude–frequency distribution, fractal dimension and spatial correlation length (SCL) of the AE hypocenters were calculated for each data set. Each parameter is a function of the time-to-failure and thus can be treated as an indicator of the critical point. It is clear that the pre-failure damage evolution prior to catastrophic failures in several common rock-types is generally characterized by: 1) accelerated energy release, 2) a decrease in fractal dimension and SCL with a subsequent precursory increase, and 3) a decrease in b-value from  1.5 to  0.5 for hard rocks, and from  1.1 to  0.8 for soft rocks such S–C cataclasite. However, each parameter also reveals more complicated temporal evolution due to either the heterogeneity of the rock mass or the micro-mechanics of shear fracturing. This confirms the potential importance of integrated analysis of two or more parameters for successfully predicting the critical point. The decreasing b-value and increasing energy release may prove meaningful for intermediate-term prediction, while the precursory increase in fractal dimension and SCL may facilitate short-term prediction.  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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