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1.
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   

2.
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   

3.
Direct core analysis results of bulk density, porosity permeability, resistivity, transit time, and strength were correlated with logging data from an oil well. The interpretations were made in terms of index values between field and laboratory data obtained for the two reservoir units studied. An engineering classification scheme was suggested. Other rock engineering properties such as sonic velocity and dynamic modulus were calculated as well. An attempt was made to predict the fracture pressure gradient (FPG) of rock formation. This work has revealed the possibility of using the direct measured data to evaluate some of the in situ rock behavior.Notations K L Liquid Permeability (m.d.) - K g Gas permeability - a Constant dependent on rock type - poissons ratio - R c Resistance of brine saturated core (ohm.m) - R w Resistivity of Brine (Salt water) (ohm.m) - I s Point Load Index value (Kg/cm2) - g accelaration constant of gravity - ac Apparant acoustic log porosity - D Apparent density log porosity - q Shaliness index - p Poisson ratio index - P o Over burden pressure (Psi)  相似文献   

4.
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   

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.
To investigate the characteristics of the sandstones under two fracture modes which are tensile fracture and shear fracture, we proposed three-point bending test and a modified shear test. Meanwhile, numerical simulations using particle flow code (PFC) and acoustic emission (AE) analysis are performed to obtain their differences. The AE hits and amplitude analyses prove that no matter which mode, they experience obvious three stages. The AE hit curve and amplitude are lower in the first stage. Then, the curve goes up steadily and the amplitude value becomes relatively large in the second stage. Entering into the third stage, the curve increases quickly to its peak value and a lot of AE signals with higher amplitude are generated. Moreover, AE b-value analysis is also used to make crack magnitude assessment. It was obvious that the distribution of b-value curve can be divided into three stages, which are just corresponding to the division of AE hits and amplitude distributions. The b-values are diverse and fluctuating largely in stage I and then show small fluctuations and have increasing trends in the whole process in stage II whereas finally exhibit sharp down to the minimum points at the stage III. The average b-values for tensile fracture tests are in the range of 0.877–1.09 whereas for shear fracture tests are within the range of 0.815–0.876. Comparing to tensile fracture, when shear fracture occurs in the rock sample, the AE energy releases faster and the proportion of large magnitude cracks is larger. The research results in this article could make more instructive and applied value to in situ non-destructive monitoring of fissure development for engineering rock mass.  相似文献   

7.
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   

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.
为研究盐岩变形破坏过程中损伤变量和分形维数之间的关系,对取自某地的纯盐岩开展了单轴压缩和三轴压缩试验。在基于声发射振铃计数的损伤模型和基于声发射定位点空间演化的分形维数计算的基础上,对盐岩变化破坏过程中的损伤变量和分形维数进行了研究。研究表明：在盐岩变形破坏过程中,盐岩分形维数逐渐降低,损伤变量逐渐增加,且分形维数下降的各个阶段与损伤变量增加的各个阶段相对应;盐岩变形破坏前分形维数不再明显下降,且不同应力状态下,盐岩变形破坏前分形维数不同;随着围压增大,盐岩变形破坏前分形维数逐渐降低,其中单轴压缩和三轴压缩应力状态时,分形维数分别低于2.42和2.31、2.20时,预示着试件内部损伤开始汇集,逐渐形成宏观破裂面,导致试件变形破坏;围压对盐岩声发射活动有明显的抑制作用,随着围压的增大,盐岩变形破坏过程中声发射活动逐渐减少,且在此过程中可以发现：在应力加载初期,盐岩分形维数快速下降时所对应的应力百分比逐渐增大,在应力加载后期,当盐岩分形维数不再明显减小时对应的应力百分比逐渐增大;在盐岩变形破坏的加载初期,损伤变量较小,能量释放较少;盐岩变形破坏前损伤变量增加较快,能量快速释放。  相似文献   

10.
Microfracturing of rock is a complicated damage evolution process. Inaccurate prediction of micro-fracturing behaviours suggests a need for the development of a better modelling method. Analysis of acoustic emission (AE) measurements in double-torsion tests indicates that micro-fracturing behaviours during the loading stage have fractal time structures. This fractal behaviour can be described by C(t) ∝ tD, where D is the correlation exponent, t is the time and C(t) is the correlation integral. Furthermore, by utilizing measured AE data, a new method has been developed to model the AE behaviours of micro-fracturing in rock, in air, and following soaking in water and in a chemical solution of DTAB. The neutral models NN (10,21,2) and NN (10,20,2) were found to describe reasonably well the AE behaviours of micro-fracturing in rock under air and DTAB conditions, and water conditions, respectively. The cumulative AE events and the cumulative AE counts predicted by the neural models agreed well with those measured in experiments. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

11.
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12.
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   

13.
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   

14.
为了研究高温条件下煤岩微裂缝发展及破坏规律，对煤样进行不同温度预损伤和三轴蠕变声发射实验，探讨煤岩在经历高温预损伤过后的力学行为特征。研究结果表明:随着温度升高，煤岩预损伤呈幂函数型递增；较低温（≤ 200℃）预损伤下，煤岩呈脆性破坏特征，加速蠕变特征不明显；较高温（>200℃）预损伤下，煤岩呈韧-脆性破坏特征，且加速蠕变特征较明显；稳态蠕变速率εs的对数值与预损伤D之间呈线性相关关系；温度越高，煤岩的声发射振铃计数率水平越小，呈低频低幅值变化，且蠕变3阶段越趋于"同频"发展，累计振铃计数Nm与预损伤D之间呈负指数型函数递减；分形维数值呈"减小-动态稳定-再次减小"3阶段变化，并与蠕变3阶段相对应，分形维数由稳态向减小转变的转折点可作为判断煤岩失稳破坏的依据；温度越高（预损伤值越大），分形维数df越大，岩样破坏越无序。研究成果对于揭示经历不同温度热解气化损伤后煤岩的长期力学行为具有重要意义。   相似文献   

15.
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   

16.
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   

17.
Hamdache  M.  Pel&#;ez  J. A.  Kijko  A.  Smit  A. 《Natural Hazards》2016,86(2):273-293

We estimate the energetic and spatial characteristics of seismicity in the Algeria–Morocco region using a variety of seismic and statistical parameters, as a first step in a detailed investigation of regional seismic hazard. We divide the region into five seismotectonic regions, comprising the most important tectonic domains in the studied area: the Moroccan Meseta, the Rif, the Tell, the High Plateau, and the Atlas. Characteristic seismic hazard parameters, including the Gutenberg–Richter b-value, mean seismic activity rate, and maximum possible earthquake magnitude, were computed using an extension of the Aki–Utsu procedure for incomplete earthquake catalogs for each domain, based on recent earthquake catalogs compiled for northern Morocco and northern Algeria. Gutenberg–Richter b-values for each zone were initially estimated using the approach of Weichert (Bull Seismol Soc Am 70:1337–1346, 1980): the estimated b-values are 1.04 ± 0.04, 0.93 ± 0.10, 0.72 ± 0.03, 0.87 ± 0.02, and 0.77 ± 0.02 for the Atlas, Meseta, High Plateau, Rif, and Tell seismogenic zones, respectively. The fractal dimension D 2 was also estimated for each zone. From the ratio D 2/b, it appears that the Tell and Rif zones, with ratios of 2.09 and 2.12, respectively, have the highest potential earthquake hazard in the region. The Gutenberg–Richter relationship analysis allows us to derive that in the Tell and Rif, the number of earthquake with magnitude above Mw 4.0, since 1925 normalized to decade and to square cell with 100-km sides is equal to 2.6 and 1.91, respectively. This study provides the first detailed information about the potential seismicity of these large domains, including maximum regional magnitudes, characteristics of spatial clustering, and distribution of seismic energy release.

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18.
Uniaxial compressive loading experiments where axial strain rate or dilatant volumetric strain rate was kept constant were carried out using a servo-controlled hydraulic testing machine. The rock studied was Oshima granite. In order to investigate the effect of the strain rate on the strength, a theory based on the assumption of redistribution of the pre-existing microcracks due to subcritical crack growth was examined. Results expected from the theory were well borne out by the observations. The strength was expressed by power-functions of both axial strain rate and dilatant strain rate. The stress corrosion index of Oshima granite appeared to be 31 ± 3, which agreed well with the values reported previously.When the axial strain rate was held constant, the acoustic emission rate increased exponentially and the b-value, the exponent in the frequency-magnitude relation of the acoustic emissions, decreased with increasing applied stress. When the dilatant volumetric strain rate was kept constant, the acoustic emission rate and the b-value remained constant and independent of the stress increase. Furthermore, when the dilatant strain rate was held constant at a higher value, the b-value was constant at a lower level. As the decrease in the b-value indicates the higher dilatant strain rate, the b-value is one of the most useful key parameters in the fracture predictions.  相似文献   

19.
Different failure modes during fracture shearing have been introduced including normal dilation or sliding, asperity cut-off and degradation. Attempts have been made to study these mechanisms using analytical, experimental and numerical methods. However, the majority of the existing models simplify the problem, which leads to unrealistic results. With this in mind, the aim of this paper is to simulate the mechanical behaviour of synthetic and rock fracture profiles during direct shear tests by using the two-dimensional particle flow computer code PFC2D. Correlations between the simulated peak shear strength and the fracture roughness parameter D R1 recently proposed by Rasouli and Harrison (2010) are developed. Shear test simulations are carried out with PFC2D and the effects of the geometrical features as well as the model micro-properties on the fracture shear behaviour are studied. The shear strength and asperity degradation processes of synthetic profiles including triangular, sinusoidal and randomly generated profiles are analysed. Different failure modes including asperity sliding, cut-off, and asperity degradation are explicitly observed and compared with the available models. The D R1 parameter is applied to the analysis of synthetic and rock fracture profiles. Accordingly, correlations are developed between D R1 and the peak shear strength obtained from simulations and by using analytical solutions. The results are shown to be in good agreement with the basic understanding of rock fracture shear behaviour and asperity contact degradation.  相似文献   

20.
Towards an understanding of joint roughness   总被引：14，自引：4，他引：10  
Summary It is argued that the currently available joint models are incapable of accurate predictions of joint shear behaviour without resorting to substantial levels of empiricism. This is because these models fail to adequately quantify joint roughness, or appreciate the importance of scale. A novel approach, which uses fractal geometry to investigate joint roughness, is described. This approach goes beyond describing the symptoms of roughness and seeks to find the cause. In the application of this approach, the concepts of fractal geometry, fractal dimension and self similarity are described and used as a framework to formulate a statistically based and practical model for the characterisation of rock joint roughness. Important relationships between the fractal dimension and the more useful statistical parameters of standard deviation of both asperity angles and asperity heights are derived. These relationships not only provide a useful, working method for quantifying joint roughness, but are also shown to provide a basis for understanding the Barton empirical JRC-JCS model. In addition, the fractal model is able to provide conceptual models for the effects of normal stress on the shear behaviour of joints and the scale-dependence of joints.  相似文献   

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