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1.
Quantification of Aperture and Relations Between Aperture,Normal Stress and Fluid Flow for Natural Single Rock Fractures 总被引:1,自引:0,他引:1
Pinnaduwa H. S. W. Kulatilake Jinyong Park Pirahas Balasingam Robert Morgan 《Geotechnical and Geological Engineering》2008,26(3):269-281
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
2.
Correlations Developed for Estimation of Hydraulic Parameters of Rough Fractures Through the Simulation of JRC Flow Channels 总被引:3,自引:1,他引:2
The hydro-mechanical response of fractured rock masses is complex, due partly to the presence of fractures at different scales.
Surface morphology has a significant influence on fluid flow behaviour of a fracture. Different empirical correlations and
statistical models have been proposed to estimate the equivalent hydraulic aperture and determine the pressure drop along
a fracture. However, the existing models suffer from not being adequately generalised to be applicable to a wide range of
real fracture surfaces. To incorporate the effect of profile roughness in the hydro-mechanical behaviour of fractured rock
masses, the joint roughness coefficient (JRC) is the most widely used empirical approach. However, the average JRC of two
fracture walls in fluid flow analysis, as is a common practice, appears to be inappropriate. It will be shown how different
combinations of pairs of JRCs could lead to a similar JRC value. Also, changing the position of the top and bottom walls of
a fracture can significantly change the hydraulic response of the fracture while the average JRC is identical in both cases.
In this paper, correlations are developed which are based on the simulation of JRCs using estimated fluid flow parameters
of 2D fractures can be estimated. In order to widen the application range of the correlations, JRC flow channels were generated:
these are 2D channels with their top and bottom walls being made from two of the JRC profiles. To estimate the JRC of linear
profiles, a correlation developed between JRC and a newly developed Riemannian roughness parameter, D
R1, is proposed. Considering ten JRC profiles, a total of 100 JRC flow channels were generated. In order to only investigate
the effect of surface roughness on fluid flow, the minimum closure between the top and bottom walls of JRC flow channels were
considered to be constant. Three cases with minimum closures of 0.01, 0.05 and 0.10 cm were considered in this study. All
JRC flow channels were subjected to fluid analysis using FLUENT software. Based on these results, correlations were developed
between the geometrical and hydraulic properties of flow channels. Analysis of several real fractures demonstrated the applicability
of these correlations. 相似文献
3.
New techniques in rock mass classification: application to welded tuffs at the Nevada Yucca Mountain
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.
5.
This study used precisely digitized standard roughness profiles to determine roughness parameters such as statistical and 2D discontinuity roughness, and fractal dimensions. Our methods were based on the relationship between the joint roughness coefficient (JRC) values and roughness parameters calculated using power law equations. Statistical and 2D roughness parameters, and fractal dimensions correlated well with JRC values, and had correlation coefficients of over 0.96. However, all of these relationships have a 4th profile (JRC 6–8) that deviates by more than ±5 % from the JRC values given in the standard roughness profiles. This indicates that this profile is statistically different than the others. We suggest that fractal dimensions should be measured within the entire range of the divider, instead of merely measuring values within a suitable range. Normalized intercept values also correlated with the JRC values, similarly to the fractal dimension values discussed above. The root mean square first derivative values, roughness profile indexes, 2D roughness parameter, and fractal dimension values decreased as the sampling interval increased. However, the structure function values increased very rapidly with increasing sampling intervals. This indicates that the roughness parameters are not independent of the sampling interval, and that the different relationships between the JRC values and these roughness parameters are dependent on the sampling interval. 相似文献
6.
JRC分形估测方法的实用性 总被引:2,自引:0,他引:2
基于分形几何的码尺法分维数与岩石节理粗糙度系数的物理意义剖析,认为D-JRC之间不存在必然的相关性.分析标准轮廓曲线的分维数,发现其分维数差级微小,难以实行粗糙度系数分级.根据实测资料阐述了岩石节理表面轮廓曲线的“自相似”是统计意义而不是绝对的,它要求JRC分形估测应统计求取,而过繁的分维数测量步骤削弱了JRC的分形统计估测的可行性.建立在实测资料统计分析基础上的JRC尺寸效应分形模型JRCn=JRC0(Ln/L0)-D客观而真实地刻画了粗糙度系数随取样长度增大而降低的规律,其中,JRC尺寸效应分维数(D)具明确的物理意义,它描述了JRC随结构面规模增大而降低的衰减速率.最后,运用JRC尺寸效应分维数(D)探讨了岩石节理粗糙度系数尺寸效应的各向异性规律. 相似文献
7.
Modeling fractured rocks with numerical methods requires some derived parameters, among which the fracture network connectivity
and the size of the representative elementary volume (REV) are both of crucial importance. Percolation and REV analyses were
made by the RepSim code. The program uses input parameters such as fractal dimension of the fracture midpoints (D
c), length exponent (E) and relative dip (α
r) data. For percolation analysis, the relative sizes of the largest percolation clusters have been calculated by stochastic
realizations of the simulated fracture networks with different parameter triplets. Furthermore, fracture networks can be classified
into three major types on the basis of their (E,D
c,α
r) parameters. For the REV calculations, the porosity of the generated fracture network was calculated. The derived REV size
of a fracture network depends essentially on input parameters and shows a decreasing tendency with increasing D and E and vice versa. The method mentioned above was tested on both metamorphic samples of the Pannonian Basin and Variscan granitoid
rocks of the Mórágy Complex. Percolation values predicted for the Mórágy granite are highly sensitive to alterations in the
input parameters. The amphibolite bodies displayed a modeled fracture network with 80 to 90% of all fractures being interconnected,
while the largest achievable percolation cluster size of gneiss is less than 10%. The REV size of the amphibolite is about
20 m as a result of connected fractures filling the whole body, while gneiss has lower porosity and higher REV (approximately
70 m). 相似文献
8.
Requirements for accurate estimation of fractal parameters for self-affine roughness profiles using the line scaling method 总被引:1,自引:1,他引:0
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.
估算岩石断裂面粗糙度的一种分形模型 总被引:3,自引:0,他引:3
提出了一种更为简单的估算岩石断裂面粗糙度值的分形模型,可用来模拟岩石断裂面剖面线。断裂面愈粗糙,其分维值也愈大,并建立了分维值与JRC值之间的经验方程。 相似文献
10.
The Shear Behavior of Bedding Planes of Weakness Between Two Different Rock Types with High Strength Difference 总被引:4,自引:2,他引:2
A. H. Ghazvinian A. Taghichian Mahmoud Hashemi S. A. Mar’ashi 《Rock Mechanics and Rock Engineering》2010,43(1):69-87
In this article, the shear behavior of discontinuities caused by bedding planes of weakness between two different rock types
with high strength difference is investigated. The effect of roughness and compressive strength of joint wall in such discontinuities
are studied. The designed profiles consist of two regular and three irregular artificial joints molded by three types of plaster
mortars with different uniaxial compressive strengths. Firstly, it is demonstrated that the shear behavior of discontinuities
with different joint wall compressive strengths (JCS) is different from rock joints with identical wall compressive strengths
by showing that Barton’s empirical criterion is not appropriate for the former discontinuities. After that, some correlation
equations are proposed between the joint roughness coefficient (JRC) parameter and some surface statistical/fractal parameters,
and the normal stress range of Barton’s strength criterion is also modified to be used for such discontinuities. Then, a new
empirical criterion is proposed for these discontinuities in such a way that a rational function is used instead of JRC log10(JCS/σ
n) as i
0(σ
c/σ
n)a/[b + (σ
c/σ
n)
a
] by satisfying the peak dilation angle boundary conditions under zero and very high normal stress (physical infinite normal
stress causing zero peak dilation angle). The proposed criterion has three surface parameters: i
0, a, and b. The reason for separation of i
0 from JRC is indicated and the method of its calculation is mentioned based on the literature. The two remaining coefficients
(a and b) are discussed in detail and it is shown that a shows a power-law relationship with b, introducing the coefficient c through b = c
a
. Then, it is expressed that a is directly related to discontinuity surface topography. Finally, it is shown that the coefficient c has higher values in irregular profiles in comparison with regular profiles and is dominated by intensity of peak dilation
angle reduction (majorly related to the surface irregularity and minorly related to roughness). The coefficient c is to be determined by performing regression analysis on experimental data. 相似文献
11.
Self-Similar and Self-Affine Properties of Two-Dimensional Fracture Patterns in Rocks 总被引:1,自引:0,他引:1
In this paper, we investigate the fractal properties of binary maps of rock fractures at different scales and different geological
types, as well as different families of fracture patterns obtained from a two-dimensional Laplacian growth model (LGM). From
these analyses we figure out which families of the LGM patterns match the structural properties of the fracture binary maps.
The LGM is defined in terms of a nonlinear map that depends on two parameters, λ and
\mathfraka\mathfrak{a}, that respectively define the area and shape of the elements of the aggregate that conforms the patterns. The fractal dimension
and roughness exponent of the LGM patterns are found to depend on
\mathfraka\mathfrak{a}, with
0 < \mathfrak a < 10<\mathfrak {a}<1. From a detailed statistical analysis of these patterns we found that the fractal dimensions of capacity, correlation and
information decrease monotonically as
\mathfraka\mathfrak{a} increases. We also found that the values of these three fractal dimensions tend to collapse on top of each other as
\mathfraka\lessapprox1\mathfrak{a}\lessapprox1. Remarkably, the fractal properties of rock fractures in the scales from millimeters up to a few meters appear to be well
represented by the fractal structure of the LGM families of patterns with
\mathfraka=0.15\mathfrak{a}=0.15 and 0.30, while the fractal properties of rock fractures in the scale of kilometers seems to be well represented by the LGM
family with
\mathfraka=0.90\mathfrak{a}=0.90. In addition, the three fractal dimension values of fracture binary maps in the scales from millimeters up to meters were
found to be different between them. Nonetheless, for fractures in the scale of kilometers, the values of the three fractal
dimensions are very close to each other as an indication of self-similar behavior. Analysis of the corrections to the scaling
of the roughness exponent, ζ, suggests that they are negligible for the LGM family of fracture patterns with
\mathfraka=0.9\mathfrak{a}=0.9. This finding points to a self-affine structure for this family of patterns. In fact, the calculated roughness exponent results
are in the range of values characteristic of rock fractures. 相似文献
12.
The perimeter-area fractal model and its application to geology 总被引:14,自引:0,他引:14
Qiuming Cheng 《Mathematical Geology》1995,27(1):69-82
Perimeters and areas of similarly shaped fractal geometries in two-dimensional space are related to one another by power-law relationships. The exponents obtained from these power laws are associated with, but do not necessarily provide, unbiased estimates of the fractal dimensions of the perimeters and areas. The exponent (DAL) obtained from perimeter-area analysis can be used only as a reliable estimate of the dimension of the perimeter (DL) if the dimension of the measured area is DA=2. If DA<2, then the exponent DAL=2DL/DA>DL. Similar relations hold true for area and volumes of three-dimensional fractal geometries. The newly derived results are used for characterizing Au associated alteration zones in porphyry systems in the Mitchell-Sulphurets mineral district, northwestern British Columbia. 相似文献
13.
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
14.
Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China 总被引:2,自引:0,他引:2
XU Jiandong HUANG Jianf WEI Fuquan YAN Yunpeng LI Yaping LIN Chien-te Institute of Geology China Earthquake Administration Beijing Chin Earthquake Administration of Fujian Province Fuzhou Fujian China China Aero Geophysical Survey Remote Sensing for Land Resources Beijing China Leader University Tainan Taiwan China 《《地质学报》英文版》2005,79(2):225-232
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 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.
The role of shear dilation as a mechanism of enhancing fluid flow permeability in naturally fractured reservoirs was mainly recognized in the context of hot dry rock (HDR) geothermal reservoir stimulation. Simplified models based on shear slippage only were developed and their applications to evaluate HDR geothermal reservoir stimulation were reported. Research attention is recently focused to adjust this stimulation mechanism for naturally fractured oil and gas reservoirs which reserve vast resources worldwide. This paper develops the overall framework and basic formulations of this stimulation model for oil and gas reservoirs. Major computational modules include: natural fracture simulation, response analysis of stimulated fractures, average permeability estimation for the stimulated reservoir and prediction of an average flow direction. Natural fractures are simulated stochastically by implementing ‘fractal dimension’ concept. Natural fracture propagation and shear displacements are formulated by following computationally efficient approximate approaches interrelating in situ stresses, natural fracture parameters and stimulation pressure developed by fluid injection inside fractures. The average permeability of the stimulated reservoir is formulated as a function of discretized gridblock permeabilities by applying cubic law of fluid flow. The average reservoir elongation, or the flow direction, is expressed as a function of reservoir aspect ratio induced by directional permeability contributions. The natural fracture simulation module is verified by comparing its results with observed microseismic clouds in actual naturally fractured reservoirs. Permeability enhancement and reservoir growth are characterized with respect to stimulation pressure, in situ stresses and natural fracture density applying the model to two example reservoirs. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
17.
P. H. S. W. Kulatilake P. Balasingam Jinyong Park R. Morgan 《Geotechnical and Geological Engineering》2006,24(5):1181-1202
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
18.
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
19.
20.
A Bonded Particle Model Simulation of Shear Strength and Asperity Degradation for Rough Rock Fractures 总被引:3,自引:3,他引:0
Mohammad Sadegh Asadi Vamegh Rasouli Giovanni Barla 《Rock Mechanics and Rock Engineering》2012,45(5):649-675
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