共查询到20条相似文献，搜索用时 31 毫秒
1.
2.
Monte Carlo simulation was used to examine the error (statistical bias) introduced in estimating a sample semivariogram through application of oriented sampling patterns to variables which are correlated with fracture orientation. Sample semivariograms of the directional components of the water velocity were used to illustrate that oriented sampling schemes can provide biased data sets which result in error in the estimation of the semivariogram, particularly in the estimation of the sill (or variance). Three sampling patterns were used to analyze directional semivariograms of the components of the fluid velocity: sampling along lines parallel to the mean regional hydraulic gradient, sampling among lines perpendicular to the mean regional hydraulic gradient, and sampling along fracture segments. The first two sampling patterns were shown to introduce substantial error in the sills of the velocity variograms. It is argued that this error is due to the combination of unequal sampling of fractures with different orientations (i.e., sampling bias) and the systematic variation in the magnitude of the velocity components with orientation of the fracture. As a consequence, it is suggested that correction factors developed to correct fracture frequency statistics need to be extended to improve estimation of spatial moments of variables which are correlated with fracture orientation. 相似文献
3.
Summary Usually, rock joints are observed in outcrops and excavation walls only as traces. Under some assumptions about the shapes of the joints and the nature of their size distributions, the underlying joint size distribution can be estimated from trace length measurements. However, the interpretation of trace length distributions from line mapping data should be approached with caution. The data are always length-biased and furthermore, the semi-trace length, the trace length, and the underlying joint size may have different distributional forms. Semi-trace length distributions are monotonic decreasing functions not sensitive to changes in the real trace length distributions. Experimental full trace length distributions are shown to have lognormal distributions and to be insensitive to major changes in the underlying joint size distributions. Under the assumptions of joint convexity and circularity a parametric model for the three-dimensional distribution of joint sizes is developed. A maximum likelihood estimation of the distribution of joint diameters, which best reflects the observed joint trace data, and corrects simultaneously for joint censoring, truncation and size bias, is developed. The theory is illustrated with numerical examples using data collected from five field sites. 相似文献
4.
The sample Dykstra?CParsons (DP) coefficient, the most popular heterogeneity static measure among petroleum engineers, may exhibit significant sampling errors. Moreover, approximations of its probability distributions (uncertainty estimates) are only available for specific families of permeability models (e.g., log-normal). The cited probability distributions allow for the specification of confidence intervals and other inferences for the theoretical DP, which will be useful for reservoir screening purposes, or to establish if a more detailed study is justified. This paper presents the development of an asymptotic approximation of the distribution of the sample Dykstra?CParsons coefficient, which is independent of the permeability probability distribution. The effectiveness (bias and confidence intervals) of the proposed approach is demonstrated using analytical and field case studies and by comparing the results gleaned with those obtained using a well-known parametric approximation, under different scenarios of reservoir maturity levels (i.e., number of wells) and different degrees of deviation from the log-normal probability density function assumption. The results show that, in the vast majority of the case studies, the proposed approach outperformed the parametric approximation; in particular, our approach resulted in a significant reduction of the bias and the confidence intervals always including the theoretical DP coefficient. In addition, an excellent agreement was observed between the asymptotic cumulative distribution of the DP coefficient and the corresponding empirical distribution for sample sizes as small as one hundred, which suggests that high success rates can be obtained when reservoirs are classified according to the asymptotic DP coefficient. 相似文献
5.
The Planar Shape of Rock Joints 总被引：1，自引：1，他引：0
Knowing the planar shape of discontinuities is important when characterizing discontinuities in a rock mass. However, the
real discontinuity shape is rarely known, since the rock mass is usually inaccessible in three dimensions. Information on
discontinuity shape is limited and often open to more than one interpretation. This paper discusses the planar shape of rock
joints, the most common discontinuities in rock. First, a brief literature review about the shape of joints is presented,
including some information on joint-surface morphology, inferences from observed trace lengths on different sampling planes,
information based on experimental studies, and joint shapes assumed by different researchers. This review shows that joints
not affected by adjacent geological structures such as bedding boundaries or pre-existing fractures tend to be elliptical
(or approximately circular but rarely). Joints affected by or intersecting such geological structures tend to be rectangular.
Then, using the general stereological relationship between trace length distributions and joint size distributions developed
by Zhang et al. (Geotechnique 52(6):419–433, 2002) for elliptical joints, the effect of sampling plane orientation on trace lengths is investigated. This study explains why
the average trace lengths of non-equidimensional (elliptical or similar polygonal) joints on two sampling planes can be about
equal and thus the conclusion that rock joints are equidimensional (circular) drawn from the fact that the average trace lengths
on two sampling planes are approximately equal can be wrong. Finally, methods for characterizing the shape and size of joints
(elliptical or rectangular) from trace length data are recommended, and the appropriateness of using elliptical joint shapes
to represent polygonal, especially rectangular, joints is discussed. 相似文献
6.
节理迹线中点密度是描述岩体露头节理分布特征的重要指标。由于露头或测窗尺寸的限制、节理迹长的差异以及露头面和节理面夹角的变化,常规的迹线中点密度计算方法通常包含尺寸、截长和角度误差。本文首先介绍了截长、尺寸和角度误差的修正原理,继而将角度误差修正系数引入到关联点密度计算方法中,提出了凸面测窗条件下同时修正截长、尺寸和角度误差的迹线中点密度计算方法。利用三维节理网络建模技术,模拟生成不同方位、不同大小和不同形状的测窗,系统分析了尺寸、截长和角度误差对迹线中点密度的影响,验证了新方法的有效性。最后,针对我国高放废物地质处置北山坑探设施的硐口岩体露头,实现了节理迹线中点密度分析。上述算例和应用表明,新方法可以有效地修正截长、尺寸和角度误差,可以为估算岩体节理分布密度提供更为可靠的依据。 相似文献
7.
由于结构面粗糙度具有各质异性、各向异性、非均一性和尺寸效应等特征，结构面粗糙度系数（JRC）取值具有不确定性，工程中广泛采用统计方法来分析结构面粗糙度性质，然而以往研究往往忽略样本数不足对统计结果的影响。针对结构面粗糙度统计测量时无法确定合理样本数的问题，分别提出基于变异系数级比分析及简单随机抽样原理的最小样本数确定方法。以实际工程岩体结构面表面数据为研究对象，对比分析两种方法在系列尺寸下确定的统计测量最小样本数。实例分析表明：小尺寸样本的变异系数（CV）值明显大于大尺寸样本，且CV值随取样尺寸的增大而减小，取样尺寸为10～50 cm的CV值基本稳定在0.31～0.47之间，取样尺寸为60～100 cm的CV值基本稳定在0.21～0.31之间；最小样本数与取样尺寸基本满足幂函数关系，且最小样本数随取样尺寸的增大而减少；系列尺寸下级比分析方法在允许误差为±2%时确定的最小样本数与简单随机抽样原理在最大允许误差为10%、置信度为95%时计算的最小样本数是一致的，相似度大于0.997。该研究方法可为工程岩体中定量获取结构面粗糙度统计测量最小样本数提供依据，保证了JRC（结构面粗糙度系数）统计测量结果的准确性，对工程岩体稳定性评价中结构面力学参数的准确获取具有重要意义。 相似文献
8.
Summary Discontinuities or joints in the rock mass have various shapes and sizes. Along with the joint orientation and spacing, the
joint persistence, or the relative size of the joint, is one of the most important factors in determining the block sizes
of jointed rock masses. Although the importance of joint persistence on the overall rock mass strength has long been identified,
the impact of persistence on rock strength is in most current rock mass classification systems underrepresented. If joints
are assumed to be persistent, as is the case in most designs, the sizes of the rock blocks tend to be underestimated. This
can lead to more removable blocks than actually exist in-situ. In addition, a poor understanding of the rock bridge strength
may lead to lower rock mass strengths, and consequently, to excessive expenditure on rock support.
In this study, we suggest and verify a method for the determination of the block sizes considering joint persistence. The
idea emerges from a quantitative approach to apply the GSI system for rock mass classification, in which the accurate block
size is required. There is a need to statistically analyze how the distribution of rock bridges according to the combination
of joint orientation, spacing, and persistence will affect the actual size of each individual block. For this purpose, we
generate various combinations of joints with different geometric conditions by the orthogonal arrays using the distinct element
analysis tools of UDEC and 3DEC. Equivalent block sizes (areas in 2D and volumes in 3D) and their distributions are obtained
from the numerical simulation. Correlation analysis is then performed to relate the block sizes predicted by the empirical
equation to those obtained from the numerical model simulation. The results support the concept of equivalent block size proposed
by Cai et al. (2004, Int. J. Rock Mech. Min. Sci., 41(1), 3–19). 相似文献
9.
Crystal Size Distributions (CSD) in Three Dimensions: Insights from the 3D Reconstruction of a Highly Porphyritic Rhyolite 总被引：7，自引：2，他引：5
Growth histories and residence times of crystals in magmaticsystems can be revealed by studying crystal sizes, size distributionsand shapes. In this contribution, serial sectioning has beenemployed on a sample of porphyritic rhyolite from a Permo-Carboniferouslaccolith from the Halle Volcanic Complex, Germany, to reconstructthe distribution of felsic phenocrysts in three dimensions inorder to determine their true shapes, sizes and three-dimensionalsize distributions. A model of all three phenocryst phases (quartz,plagioclase, K-feldspar) with 217 crystals, and a larger modelcontaining 1599 K-feldspar crystals was reconstructed in threedimensions. The first model revealed a non-touching frameworkof crystals in three dimensions, suggesting that individualcrystals grew freely in the melt prior to quenching of the texture.However, crystal shapes are complex and show large variationon a Zingg diagram (intermediate over long axis plotted againstshort over intermediate axis). They often do not resemble thecrystallographic shapes expected for phenocrysts growing unhinderedfrom a melt, indicating complex growth histories. In contrast,the three-dimensional size distribution is a simple straightline with a negative slope. Stereologically corrected size distributionsfrom individual sections compare well with stereologically correctedsize distributions obtained previously from the same sample.However, crystal size distribution (CSD) data from individualsections scatter considerably. It is shown that CSDs can berobustly reproduced with a sampling size of greater than 200crystals. The kind of shape assumed in stereological correctionof CSDs, however, has a large influence on the calculation andestimation of crystal residence times. KEY WORDS: 3D reconstruction; crystal shapes; CSD; porphyritic rhyolite; quantitative petrography 相似文献
10.
Michael S. Riley 《Mathematical Geology》2004,36(6):683-702
A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case. 相似文献
11.
Sampling elongate clasts that protrude from a planar face for clast macro‐fabric analysis introduces a bias into reconstructed fabrics because clasts aligned perpendicular to the sampling face are over‐represented relative to those aligned parallel to the face. This study develops a probability‐based mathematical analysis to quantify sample bias for a variety of clast shapes and population fabrics, including isotropic, clustered and girdled fabric styles. Bias is expressed in terms of sample eigenvalues and eigenvectors relative to those of the parent population. Results indicate that sampling always has the effect of artificially drawing fabrics towards perpendicularity to the sampling face relative to the populations from which they are drawn. This rotation generally has the effect of artificially strengthening population fabrics, by up to 30% in the case of very weakly clustered or girdled populations. However, fabric strengthening is by no means universal and sampling alters different parent populations in different, sometimes complex, ways: the analysis in this paper identifies situations where sampling can strengthen or weaken parent fabrics, where it can rotate parent fabrics (by up to 90° in the case of a very weak population fabric), and where it can even change the style of a population fabric. For example, near‐isotropic population fabrics can appear clustered; weakly clustered and weakly girdled population fabrics can appear isotropic; weakly clustered population fabrics can appear weakly girdled; and girdled population fabrics can appear clustered. Overall, this analysis indicates that weakly orientated population fabrics are most susceptible to bias. Thus, a weakly clustered population fabric aligned parallel to a sample face is particularly susceptible to major sample bias in both fabric strength (artificially overestimated) and orientation (artificially rotated perpendicular to the face). Bias can be reduced either by sampling all the clasts from a cube‐shaped block of sediment excavated from the face, or by sampling equal numbers of clasts from the three orthogonal faces of the same sedimentary unit. 相似文献
12.
This paper presents a new method for determining the structural domain boundaries within the rock mass. This new method is based on a statistical comparison of data from pairs of sample regions. The stereonet is divided into 100 windows with approximately equal areas. The poles of joints occurring in each corresponding window on the two projection plots of the regions being compared are then merged and arranged in ascending order with respect to their trace lengths. Finally, the Wald–Wolfowitz runs test is used to identify the homogeneity of structural populations by analyzing the joint sequence. Based on a significance level of 0.01, the homogeneity of structural populations collected from four adjacent adits at the Songta dam site is determined using the proposed method. The results show that the boundaries of structural domain change with the sizes of the sampling domains being compared. The initial sampling domains should be selected according to the engineering geological conditions of the studied area. In addition, the clear advantage of the proposed method is that both joint orientation and trace length are considered. 相似文献
13.
三维剖面地质界线是构建三维地质结构模型的重要基础数据,其不确定性会影响三维模型的几何形态和属性分布。以单一分布为假设前提的统计学不确定性分析方法掩盖了其他概率分布特征对模型的影响。突破单一误差分布条件的假设前提,本文使用Monte Carlo方法模拟了不同概率分布情况下地质剖面数据中地质界线的抽样采集,以及地质界线空间分布的不确定性;依托地质界线空间位置与地质属性的耦合关系,提出了用地质属性概率分布实现地质界线空间不确定性的定量可视化,并结合实际地质剖面探讨了多种概率分布条件下地质界线的空间不确定性。实例研究表明,基于Monte Carlo模拟的不确定性分析方法可以突破单一误差分布假设条件,结合地质属性概率可充分揭示出建模数据的内在不确定性与模型外在要素形态之间的耦合关系。 相似文献
14.
Box fractal dimension as a measure of statistical homogeneity of jointed rock masses 总被引：2，自引：0，他引：2
Pinnaduwa H. S. W. Kulatilake Reno Fiedler Bibhuti B. Panda 《Engineering Geology》1997,48(3-4):217-229
A written computer programme to estimate the box fractal dimension (DB) is verified by estimating DB of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated DB is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated DB. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of DB. By calculating DB for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that DB can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of DB along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of DB is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of DB. It is recommended that the spatial variation of DB is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses. 相似文献
15.
Pinnaduwa H. S. W. Kulatilake 《Mathematical Geology》1986,18(2):181-195
A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a 2 goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the 2 test results of theIXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters
and
, based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method. 相似文献
16.
Basanta K. Sahu 《Sedimentary Geology》1976,16(3):177-192
Currently popular line and ribbon methods yield grain counts that are differentially biassed in regard to sizes and orientations of the maximum projection diameter of the grains in the sample. Bias correction factors covering the entire range of counting situations are obtained using probability theory and coordinate geometry. The corrected numbers are true unbiassed Fleet counts that are suitable for estimating true statistical measures and for estimating economic potential of mineral(s). Irregular grains can be counted by classifying them into either elliptical or rectangular shapes by means of nondimensional discriminant equations based on area or length measurements. Wadell roundness (ρ) for elliptical and rectangular outlines shows inconsistency, but the modified Wadell roundness (ρ′) proposed herein is a consistent measure of roundness for all types of shapes, and hence the latter is recommended for use. Theoretically, roundness is linearly correlated with the form factor (B/A) for elliptical outlines and hence, a linear correlation of average roundness and average form factor in sediments is to be expected. The entire spectrum of shape comprising two continuous variables, form factor and modified Wadell roundness, may be classified into two discrete shape states (elliptical and rectangular) or into several discrete shape states having ranges of ρ′ and B/A values. 相似文献
17.
Estimating Mean Fracture Trace Length and Density from Observations in Convex Windows 总被引：19，自引：3，他引：16
M. Mauldon 《Rock Mechanics and Rock Engineering》1998,31(4):201-216
Summary Although window samples of fracture traces are widely recognized to be length-biased and censored, they are often the best
source of data for inferring statistical parameters of fracture sets. This paper presents new estimators for mean fracture
trace length and density that correct for the effects of bias and censoring. A stereological estimator of mean trace length
is derived for parallel traces in a rectangular sampling window, an end-point estimator of mean trace length is derived for
windows with arbitrary convex boundaries and for arbitrary trace length distributions, and an end-point estimator of trace
density is derived for windows with arbitrary convex boundaries and for arbitrary trace length and trace orientation distributions.
Results for rectangular and circular windows are obtained as special cases of the general solutions for arbitrary convex windows.
When applied to circular windows, the end-point estimator of mean trace length is, in addition, independent of the trace orientation
distribution. The estimators are easily determined from field data. The end-point estimator of trace density requires knowing
only the area of the window and the number of end-points inside the window. The end-point estimator of mean trace length,
when applied to circular windows, requires, in addition, the number of end-points outside the window (of those traces that
intersect the window) and the stereological estimator of mean trace length requires only the apparent mean trace length and
the height of the window. 相似文献
18.
Progressively censored sampling of rock joint traces 总被引：1，自引：0，他引：1
Gregory B. Baecher 《Mathematical Geology》1980,12(1):33-40
A number of sampling problems in geology and engineering geology involve geometric variables, and must deal with the almost pervasive biases that accompany geometric sampling. Among these biases is the fact that not all elements of the sampled population are fully observable. Some members, usually the largest, are censored. Inferences cannot ignore the censored members of the sample, because the censoring is often related to the variable being inferred—for example, the case of sampling for feature size. Inferences from samples are conceptually straightforward, and for the simple case of exponential parent distributions, mathematically tractible. Maximum likelihood and Bayesian results are given for the exponential case, and examples are drawn from joint surveys in rock mechanics. 相似文献
19.
A new surface-sampling technique for unconsolidated sands on aeolian dunes is introduced and analyzed in terms of an elementary mathematical model. The sampling bias inherent to the technique is modeled using a simple geometric argument. This shows that samples drawn from 2D slices of a 3D population are naturally biased toward larger sand grains, with the nth moment of the surface (2D) distribution proportional to the (n+1)th moment of the bulk (3D) distribution. Laboratory tests of the sampling technique allow an empirical relation for the sampling bias to be determined, and comparison shows the model and empirical relations to be in close agreement for the particular population distributions considered. Possible corrections to the model, as suggested by the empirical analysis, are also discussed. 相似文献
20.
The present paper addresses statistical analysis and estimation of fracture-length distributions at scales influenced by the truncation and censoring effects. The computational method employed here uses fracture-length distributions of a given set of measurements and information about observational constraints (i.e., window of observation) to estimate the probability density of the truncated and censored parts of fracture data sets. The results are benchmarked against power-law based maximal likelihood estimations commonly used for the same purpose. The relationship between the accuracy of estimates and size of the window of observation is studied. The utility of employing statistical models with arbitrary probability distributions of fracture lengths in order to provide a valid statistical model approximation is also considered. A verification of the suggested approximation using the Kolmogorov–Smirnov test applied to truncated and censored data is proposed. Numerical computations show that the proposed method can represent an essential improvement compared to other commonly employed techniques. 相似文献