共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
Estimation of mean trace length of discontinuities 总被引：18，自引：0，他引：18
Summary Trace lengths of discontinuities observed on finite exposures are biased due to sampling errors. These errors should be corrected in estimating mean trace length. A technique, which takes into account the sampling errors, is proposed for estimating the mean trace length on infinite, vertical sections from the observations made on finite, rectangular, vertical exposures. The method is applicable to discontinuities whose orientation is described by a probability distribution function. The method requires that the numbers of discontinuities with both ends observed, one end observed, and both ends censored be known. The lengths of observed traces and the density function of trace length are not required. The derivation assumes that midpoints of traces are uniformly distributed in the vertical plane. Also independence between trace length and orientation is assumed. Data on a Pennsylvania shale in Ohio, U. S. A., were used as an example.Notations
dip direction
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direction of sampling plane
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acute angle between dip direction and sampling plane
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dip angle
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A
apparent dip angle
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mean density of trace mid-points per unit area
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mean trace length
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D
diameter of discontinuity
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f (.),g (.)
probability density function
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h
height of rectangular window
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estimator of mean trace length
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m
sample size, number of discontinuities intersecting window
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m
0
number of discontinuities intersecting window with both ends censored
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m
2
number of discontinuities intersecting window with both ends observed
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n, N
expected number of discontinuities intersecting the window
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n
0,N
0
expected number of discontinuities intersecting the window with both ends censored
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n
2,N
2
expected number of discontinuities intersecting the window with both ends observed
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Pr (.)
probability
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w
width of rectangular window
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x
trace length 相似文献
3.
《Journal of Structural Geology》2001,23(2-3):247-258
We introduce new estimators for fracture trace intensity, trace density and mean trace length that exploit the use of circles as efficient sampling tools. A fracture trace is the commonly observed surface expression of a fracture, i.e. the intersection of a fracture with an exposed surface such as a rock pavement or a mine drive wall. Trace intensity, trace density and mean trace length estimators are derived and shown to form a self-consistent set of two-dimensional fracture abundance measures. The intensity estimator n/4r uses the number, n, of intersections between fracture traces and a circular scanline of radius r. The density estimator m/2πr2 uses the number, m, of trace endpoints inside a circular window. The mean trace length estimator (n/m)πr/2 uses the ratio of the number of trace intersections on the circle to the number of endpoints in the circle.The circular sampling tools and estimators described here eliminate most sampling biases due to orientation and also correct many errors due to censoring and length bias that plague established scanline and areal measurement techniques. Performance of the estimators is demonstrated by comparison with areal samples of a synthetic fracture trace population with known intensity, density and mean trace length. The estimators are also applied successfully to a natural rock pavement with two orthogonal fracture sets, one of which is severely censored. Because the new circle-based estimators only require counts of trace–circle intersections and/or trace endpoints, they are more time-efficient than current methods for estimating geometric characteristics of fracture traces. 相似文献
4.
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
5.
S. D. Priest 《Rock Mechanics and Rock Engineering》2004,37(5):347-368
Summary The paper outlines a new method for estimating the distribution form, and mean size, of discontinuities from scanline data. By assuming that the discontinuities are circular discs it has been possible to apply existing solutions for the distributions of censored semi-trace lengths sampled by a scanline at an exposed rock face. These solutions have been implemented by numerical quadrature in a standard Excel spreadsheet, with solution optimisation achieved with Solver. Problems caused by a singularity in the integration were overcome by applying an integration offset parameter. A trigonometrical substitution for removing this singularity is also outlined. The numerical quadrature strategy was validated by comparison with the analytical solution for the uniform distribution, and by comparison with the results of an extensive geometrical simulation of the stereological process. A new distribution, here named the Wicksell distribution, has been identified. This distribution is characterised by the fact that the distribution of disc diameters and the distribution of complete traces on a cutting plane are identical. Two examples, based on real scanline data, are presented to illustrate the practical application of the new methods. 相似文献
6.
The equations that exist in the literature to estimate corrected mean trace length and corrected two-dimensional density of a rock discontinuity set using area sampling technique are critically reviewed. The discontinuity traces appearing in an outcrop in Yingxiu area in China are used along with rectangular windows to calculate the corrected mean trace length and two-dimensional density using Kulatilake and Wu’s equations. Similarly, circular windows are used along with Mauldon’s and Zhang and Einstein’s equation to calculate the mean trace length and Mauldon’s equation to calculate the two-dimensional density for the same discontinuity sets using the same outcrop discontinuity trace data. For both parameters, the predictions based on the rectangular window methods were found to be more accurate than that based on the circular window methods. 相似文献
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不连续面平均速长概率估值法及其应用 总被引：4，自引：1，他引：4
在进行不连续面3-D网络模拟过程中, 不连续面的大小是一个重要的参数, 该数据主要来源是在现场露头上测量不连续面出露的迹长。由于取样中不可避免的偏差而使结果有误差, 在进行平均迹长估计时取样的误差必须予以校正, 本文介绍一种用概率的方法考虑取样误差通过有限2-D露头上测量的不连续面数据求算无限2-D空间平均迹长的技术。该方法可以借助计算机进行处理。 相似文献
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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
14.
从不连续面与窗口交切的充要条件出发,推导了窗口法不连续面剖面测量的平均迹长估算公式,实例分析表明用雇在算的平均迹长与实测平均迹长吻合较好。 相似文献
15.
结构面平均迹长估算的Laslett算法和广义H-H算法虽然在理论上具有严密的推导过程,但实际应用时,由于迹长层次不同,两种算法估值精度不同。在利用开挖边坡所揭露的全迹长资料对不同迹长层次下两种算法的估值精度进行检验的基础上,讨论了两种算法的适用性,并针对工程中所采用的测量窗口高度通常较小这一实际情况,对广义H-H算法在小窗口长迹长层次下的迹长估计值进行适当修正。综合研究结果,建议:(1)小窗口短小迹长层次情况下采用Laslett算法进行迹长估计; (2)小窗口长大迹长层次情况下采用乘以修正系数x=2的广义H-H算法。 相似文献
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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
19.
《Journal of Structural Geology》1997,19(6):835-847
Fracture mechanics theory and field observations together indicate that the shear stress on many faults is non-uniform when they slip. If the shear stress were uniform, then: (a) a physically implausible singular stress concentration theoretically would develop at a fault end; and (b) a single curved ‘tail fracture’ should open up at the end of every fault trace, intersecting the fault at approximately 70 °. Tail fractures along many small faults instead range in number, commonly form behind fault trace ends, have nearly straight traces and intersect a fault at angles less than 50 °. A ‘cohesive zone’, in which the shear stress is elevated near the fault end, can eliminate the stress singularity and can account for the observed orientation, shape, and distribution of tail fractures. Cohesive zones also should cause a fault to bend. If the cohesive zone shear stress were uniform, then the distance from the fault end to the bend gives the cohesive zone length. The nearly straight traces of the tail fractures and the small bends observed near some fault ends implies that the faults slipped with low stress drops, less than 10% of the ambient fault-parallel shear stress. 相似文献
20.
Discontinuities such as fractures or cracks are common in geo-materials. Connectivity is a comprehensive parameter that includes the influence of length, orientation and density of the discontinuities. The main objectives of this paper are to define connectivity based on the statistical geometrical parameters of a network of random discontinuities and to quantify the hydraulic properties of the network using connectivity. An analytical method is first proposed to evaluate connectivity through the density of degree of freedom (DDOF). The analytically estimated DDOF is verified using numerical analysis. DDOF increases with the increases in the mean length, relative orientation and density of the random discontinuity network. Connectivity becomes better and the permeability becomes larger with increasing DDOF. The representative element volume (REV) of a random discontinuity network can be estimated based on connectivity. When a discontinuity network is poorly connected, a REV does not exist when the size of the discontinuity network is smaller than 10 times of the mean length of the discontinuities. When a discontinuity network is normally connected, a REV exists when the REV size is smaller than 10 times of the mean length of the discontinuities. When the discontinuity network is highly connected, the REV size is only 2–4 times of the mean length of the discontinuities. The results indicate that DDOF is a good indicator to quantify the connectivity of a random discontinuity network and the relationship between connectivity and permeability. 相似文献