岩体表面节理迹长与节理真实长度尺寸的概率关系

空间节理长度不能直接进行测量,只能通过岩石暴露面上节理迹线长度来量测,但是节理迹线是节理面与岩面交切的结果,迹长在多大程度上能代表节理真实长度是值得研究的,本文利用计算机模拟的方法分析了迹长与节理真实长度的统计关系。     

Maximum likelihood classification for facies inference from reservoir attributes

A cluster analysis methodology is developed to recover facies realizations from observed reservoir attributes. A maximum likelihood estimator allows us for identifying the most probable underlying facies using a spatial clustering algorithm. In seismic characterization, this algorithm can yield relevant geological models for subsequent history-matching studies. In history-matching procedures, it provides informative facies maps as well as starting points for further studies.     

基于裂隙产状和迹长划分岩体统计均质区研究

岩体统计均质区的划分是岩体工程设计的首要步骤,因为不同的均质区内岩体的结构特性和力学特性都存在差异。大多研究考虑产状或者其他单一参数划分岩体统计均质区,却很少有人考虑多参数进行划分研究。考虑了裂隙产状、迹长两个参数,提出了一种划分裂隙岩体统计均质区的新方法,即基于秩和检验评价两个样本之间的相似性,从而实现对裂隙岩体统计均质区的划分。结合工程实例即云南省马吉水电站左岸坝肩某两高程4个平硐的岩体结构统计均质区划分,分析了多参数对裂隙岩体统计均质区划分的影响。研究结果表明：PD241和PD253、PD201和PD241分别划分为一个统计均质区,而PD201和PD251 以及PD251和PD253不具有统计相似性。考虑了产状和迹长因素对岩体统计均质区的影响,划分结果较Miller方法更加合理可靠。结合现场调查分析,新方法的结果更加吻合实际情况。     

Estimation of joint trace length probability distribution function in igneous,sedimentary, and metamorphic rocks

To predict the behavior of structures in and on jointed rock masses, it is necessary to characterize the geomechanical properties of joints and intact rock. Among geometry properties of joints, trace length has a vital importance, because it affects rock mass strength and controls the stability of the rock structures in jointed rock masses. Since joint length has a range of values, it is useful to have an understanding of the distribution of these values in order to predict how the extreme values may be compared to the values obtained from a small sample. For this purpose, three datasets of joint systems from nine exposures of igneous, metamorphic, and sedimentary rocks are studied. Joint trace length is one of the most difficult properties to measure accurately, but it may be possible to record other geometrical properties of exposed joints accurately; thereby, support vector machine (SVM) model is used to predict the joint trace length. SVM is a novel machine learning method, which is a powerful tool used to solve the problem characterized by small sample and non-linearity with a good generalization performance. Consequently, goodness-of-fit (GOF) tests were applied on these data. According to these GOF tests, the lognormal distribution was found to be the best probability distribution function for representing a joint trace length distribution.     

Demarcation of homogeneous structural domains within a rock mass based on joint orientation and trace length

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.     

Comparison of rock discontinuity mean trace length and density estimation methods using discontinuity data from an outcrop in Wenchuan area,China

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.     

Optimal estimation of in-situ ground stresses from displacement measurements

This paper presents a study on the optimal estimation of initial in-situ stresses, in which the in-situ stresses may be constant or linearly changing along a co-ordinate axis, from a set of relative measurements between adjacent measuring points utilized for monitoring the stability of tunnels. Displacements occurring before installation of measuring devices can be taken into account. The approach may be used for a variety of models used to simulate the ground media through which the tunnels are being excavated and has the advantage of being easy to implement on the computer and having both good precision and calculation stability. Finally, an analysis is carried out on the stability of the algorithm and computational time for different numerical examples.     

Estimation of mean trace length of discontinuities

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 - direction of sampling plane - acute angle between dip direction and sampling plane - dip angle - _A apparent dip angle - mean density of trace mid-points per unit area - mean trace length - D diameter of discontinuity - f (.),g (.) probability density function - h height of rectangular window - estimator of mean trace length - m sample size, number of discontinuities intersecting window - m ₀ number of discontinuities intersecting window with both ends censored - m ₂ number of discontinuities intersecting window with both ends observed - n, N expected number of discontinuities intersecting the window - n ₀,N ₀ expected number of discontinuities intersecting the window with both ends censored - n ₂,N ₂ expected number of discontinuities intersecting the window with both ends observed - Pr (.) probability - w width of rectangular window - x trace length     

Determination of stiffness and other joint properties from roughness measurements

Summary The measurement of surface profiles is presented as a useful and simple approach to classifying statistically the essential features of rock joints. After introducing the reader to some existing analytical joint contact models for normal loading, a discrete numerical technique is developed. Using this technique the mechanical behaviour of a number of different slate joints is examined. The functional relationships between nominal stress, stiffness, true contact area and initial aperture are shown, for this class of joints, to be surprisingly simple. Experimental evidence is used to substantiate the numerical results. From the point of view of in-situ joint stiffness and hydraulic conductivity, numerical predictions seem feasible provided the degree of mating at some known stress level can be determined.     

Computationally efficient restricted maximum likelihood estimation of generalized covariance functions

Computational aspects of the estimation of generalized covariance functions by the method of restricted maximum likelihood (REML) are considered in detail. In general, REML estimation is computationally intensive, but significant computational savings are available in important special cases. The approach taken here restricts attention to data whose spatial configuration is a regular lattice, but makes no restrictions on the number of parameters involved in the generalized covariance nor (with the exception of one result) on the nature of the generalized covariance function's dependence on those parameters. Thus, this approach complements the recent work of L. G. Barendregt (1987), who considered computational aspects of REML estimation in the context of arbitrary spatial data configurations, but restricted attention to generalized covariances which are linear functions of only two parameters.     

Fractographic determination of joint length distribution in chalk

Summary Measurements of fracture joint distribution combined with determinations of plume length and orientation on a vertical section of a single chalk layer near Beer Sheva, Israel, reveal that joints marked by unilateral and circular plumes are skewed towards the shorter sizes while joints decorated by bilateral plumes are skewed towards the longer sizes. The mean lengths of the unilateral and bilateral joints are 66.5 cm and 155.6 cm, with standard deviations of 30 cm and 60.6 cm, respectively. These results as well as joint length observations from other areas seem to suggest a bimodal length distribution. However, since the minor maximum is generally very weak, and due to some additional uncertainties, further confirmation of the present observations is needed.     

Quantifying the uncertainty of semiarid flash floods using generalized likelihood uncertainty estimation

This paper aims to address the question of how the parameter uncertainty associated with a mixed conceptual and physical based rainfall-runoff model (AFFDEF) has influences on flood simulation of the semiarid Abolabbas catchment (284 km²), in Iran. AFFDEF was modified and coupled with the generalized likelihood uncertainty estimation (GLUE) algorithm to simulate four flash flood events. Analysis suggests that AFFDEF parameters showed non-unique posterior distributions depending on the magnitudes and duration of flash flood events. Model predictive uncertainty was heavily dominated by error and bias in soil antecedent moisture condition that led to large storage effect in simulation. Overall, multiplying parameter for the infiltration reservoir capacity and multiplying parameter for the interception reservoir capacity along with potential runoff contributing areas were identified the key model parameters and more influential on flood simulation. Results further revealed that uncertainty was satisfactorily quantified for the event with low to moderate flood magnitudes while high magnitude event exhibited unsatisfactory result.     

Determination of the distribution of size of irregularly shaped particles from laser diffractometer measurements

The formal stereological transformation equation for particle sieve size distribution from measurements in lower dimensional spaces is applied to laser diffractometer measurements. The transformation function for iron ore particles is measured experimentally, and modeled. The solution is tested against the measured transformation function data as well as synthetic composite distributions of the original sample. The natural size distribution of a sample taken from a grinding circuit stream was measured by a combination of standard sieving and cyclosizer, and the result is compared to the transformed size distribution calculated from laser diffractometer measurements. The stereological transformation technique performed well in all cases.     

Aquifer hydraulic conductivity estimation from surface geoelectrical measurements for Krauthausen test site, Germany

The physical explanation is presented for two types of theoretical equations which encompass a direct and an inverse relationship between the hydraulic conductivity and electrical resistivity of an aquifer. Using the theory of direct current (DC) resistivity prospecting, it is shown that a direct relation exists if the bulk of the current flow is in the vertical direction, whereas the inverse relation exists if the current is in the horizontal direction. Consequently, the relation in question is direct in the case of a relatively conducting basement and inverse in the case of a comparatively resistive basement. Then, the aquifer hydraulic conductivity for the hydrogeologically well-studied area of Krauthausen in Germany is estimated by two different techniques using surface geoelectrical data. The estimated values are compared with those conventionally determined by a pump test experiment and it can be concluded that the estimation is better whenever geoelectrical data are used.     

Proton-induced X-ray emission measurements of trace elements in water samples collected from an Indiana coal mining locality

A new method of simultaneous multi-elemental analysis, Proton Induced X-ray Emission (PIXE), was used to detect trace elements in waters associated with a coal strip-mining operation in southern Indiana. Stream, pond, and ground water samples were collected and analyzed monthly from, or near, Sulphur Creek in Sullivan County. The concentrations of 26 major and trace elements were determined in samples from eleven locations: K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, As, Se, Br, Rb, Sr, Mo, Cd, Sn, Sb, I, Ba, Hg, Pb, and U. Elemental concentrations fluctuated considerably throughout the 13-month sampling period and also among sampling sites. Nickel, Zn, As, Cd, Mn, Fe, and Ca were highest in the upstream water which was most acidic (pH = 2.9–4.0) because of old unreclaimed mining operations. The highest values recorded were Ni = 1662 ppb, Zn = 4953 ppb, As = 26 ppb, Cd = 93 ppb, Mn = 5063 ppb, Fe = 63 ppm, and Ca = 325 ppm. The concentrations of these elements decreased downstream as the pH of Sulphur Creek increased which was likely due to the influence of the calcareous glacial till cover in the area and the recent mining activity which disturbed overburden containing a high percentage of calcareous materials. Lead, I, Br, and Ti values were highest (661 ppb, 86 ppb, 70 ppb, and 45 ppb, respectively) in the ground water from the coal seam (pH approximately 7). Other elements which were relatively high in the pH 7 waters closest to the current mining operations (pond, stream, and groundwater) included K (17 ppm), Sr (3408 ppb), Ba (173 ppb), As (14 ppb), Rb (16 ppb), Sn (14 ppb), and Cu (3840 ppb). The highest Cu concentration was recorded at the point where drainage water from the mine entered Sulphur Creek. Gallium, U, Hg, and Mo were found in low (< 13 ppb for Ga and Hg; < 205 ppb for Mo and U) concentrations and only in the ponds within the mine.     

Nonparametric estimation of multivariate joint and conditional spatial distributions

To estimate the recoverable reserves of deposits containing more than one metal, linear combinations of sample grades based on the economic importance of each metal have been employed. These linear combinations, called equivalent grades, have inherent problems at least one of which is that the contribution of an individual metal is confounded with all others. As an alternative to equivalent grades, multivariable joint and conditional spatial distributions may be estimated using indicator variable methods. These spatial distributions may then be used to determine the joint or conditional amounts of the metals in the estimated recoverable reserve.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.     

The effect of sample size on geological strain estimation from passively deformed clastic sedimentary rocks

The role of sample size in the estimation of geological strain, both finite strain (R_s) and that of the orientation of the finite strain ellipse (φ_s), is investigated for clastic sedimentary rocks. This study looks at four strain methods, the Robin method, the linearization method, the Mulchrone and Meere method and the mean radial length method that are initially tested using simulated strained data sets and subsequently by applying the methods to real data. It is found that the optimum strain analysis sample size for a clastic sedimentary rock is primarily dependant on the intensity of strain suffered by that rock because of the error behavior associated with R_s estimates. An iterative process is therefore recommended starting with a minimum sample size of 150, which can be maintained or reduced based on the initial R_s estimates.     

岩体不连续面迹长与直径间的概率关系模型分析

由于“随机”概念的模糊性,在假定不连续面为薄圆盘及弦长作为迹长的前提下,基于迹线端点在圆周上均匀分布、迹线中点在直径上均匀分布、迹线中点在圆面域内均匀分布这3种明确而又不同的“随机”含义,可以得到3种合理的迹长 与直径 间的概率关系模型。通过对这3种模型进行分析认为：其在各自的“随机”含义下都是正确的,只是适用条件各异;野外实际可行的条件是介于模型2 和模型3之间的,合理地分析应该同时考虑这两种模型。在实际应用中,应该首先对所有取样面产状之间的关系进行分析,根据其结果来分配给模型2和模型3以某种权重,这样得到的迹长与不连续面直径之间概率关系更具合理性,其结果弥补了目前国内外进行的相关研究仅仅考虑到第2类模型的不足。     

On the theory of the evaluation of joint orientation measurements

SummaryOn the Theory of the Evaluation of Joint Orientation Measurements The current procedure for the evaluation of sets of joint-orientation measurements in terms of regional stresses is critically reviewed. It is shown that the counting circles on a sphere for constructing density diagrams are not circles on an equal-area (Lambert) projection of such a sphere; the correct curves are presented. It is shown that the search for modal maxima in the density diagrams corresponds to a nonparametric statistic for which it is difficult to give confidence limits. General considerations about the statistics of experiments yield the result that 12–15 joint measurements in an outcrop are sufficient to define 3 maxima, if such maxima exist at all.In order to give confidence limits, it is best to introduce a parametric model for the distribution of joint orientations. For a single cluster of orientations the probability density function is chosen as proportional to exp (k ² cos² ) where is the polar deviation angle from the mean direction; since the basic joint-orientations havethree fundamental directions, three probability density functions of the above type have to be superposed. These are determined by giving 11 parameters which can be determined by a function-minimization procedure from a given set of measurements. This procedure is best carried out on a computer. In this fashion, confidence limits for the preferred joint directions can be obtained.For the determination of the stresses, only two preferred sets of joints are required reducing the necessary number of parameters to 7. According to the usual theory of the statistics of trials, it is seen that 21 measurements are required to determine them. Thus, using a parametric statistic, it is seen that 21 measurements of joint orientations in an outcrop should suffice to determine the stress field that produced them. If the sharpness of the distributions is assumed as a priori known, this reduces again to the 15 or 20 measurements required for a non-parametric evaluation.

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ZusammenfassungZur Theorie der Auswertung von Kluftstellungsmessungen Die gegenwärtig übliche Methode zur Auswertung von Kluftstellungsmessungen wird kritisch untersucht. Es wird gezeigt, daß die Zählkreise auf der Einheitskugel zur Bestimmung von Kluftpoldichten auf dem Lambertschen Netz keine Kreise ergeben; die richtigen zu benützenden Zählfenster sind in der Arbeit abgebildet. Es wird gezeigt, daß die Bestimmung von Poldichtemaxima einer nichtparametrischen statistischen Methode entspricht, für welche es schwierig ist, Vertrauensgrenzen anzugeben. Allgemeine Betrachtungen über die Statistik von Experimenten ergeben das Resultat, daß zur Bestimmung von 3 Kluftpolmaxima in einem Poldichtediagramm für einen Aufschluß nur 12–15 Kluftmessungen notwendig sind, wenn solche Maxima überhaupt existieren.Um Vertrauensgrenzen anzugeben, ist es am besten, ein parametrisches Verteilungsmodell für die Kluftstellungen einzuführen. Für einen Polhaufen mit einem einzigen Maximum wird die Dichtefunktion proportional zu exp (k ² cos² ) gewählt, wo die Poldistanz von der Richtung des Maximums bedeutet. Da man im allgemeinen für den Kluftkörper drei charakteristische Kluftstellungen erwartet, muß die Dichtefunktion durch die Überlagerung dreier Funktionen obigen Typs gebildet werden. Eine solche wird dann durch 11 Parameter spezifiziert, welche durch eine Funktionsminimisierung aus einer Meßserie bestimmt werden können. Die Minimisierung wird am besten auf einem Elektronenrechner ausgeführt; man erhält auf diese Weise Vertrauensgrenzen.Zur Bestimmung der Spannungen braucht man nur zwei Polmaxima, so daß sich die Zahl der zu bestimmenden Parameter auf 7 reduziert. Nach der üblichen Theorie der Statistik der Experimente benötigt man dann 21 Kluftstellungsmessungen an einem Aufschluß. Die parametrische Betrachtungsweise führt daher zum Resultat, daß man nur 21 Kluftmessungen benötigt, um das Spannungsfeld, das die Klüfte produzierte, zu bestimmen. Wenn die Schärfe der Verteilungen als gegeben angenommen wird, reduziert sich die Zahl weiter bis auf etwa 15 Messungen, was wieder der aus nichtparametrischen Betrachtungen abgeleiteten Zahl entspricht.

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RésuméContribution à la théorie de l'évaluation des déterminations de l'orientation des clivages Une revue critique de la méthode actuellement en usage pour l'évaluation des déterminations des orientations des clivages dans un affleurement est donnée. Il est démontré que les cercles sur une sphère d'unité ne deviennent pas des cercles dans une projection de Lambert; les figures correctes sont présentées; il faut les utiliser pour déterminer la densité des pôles des clivages dans un graphe. Les maxima de densité des pôles sont ainsi déterminés par une méthode non-paramétrique pour laquelle il est difficile de donner des limites de confiance. Des considérations générales concernant la statistique des épreuves donnent le résultat qui'l ne faut que de 12 à 15 déterminations individuelles de clivages pour déterminer les 3 maxima du parallelépipède fondamental de la roche; — si ces maxima existent.Afin d'obtenir les limites de confiance, il faut choisir une méthode paramétrique où l'on donne une distribution hypothétique pour les orientations des clivages. Pour une seule accumulation des pôles, on prend une distribution proportionale à exp (k ² cos² ) où est la distance polaire entre la direction du maximum et la direction considérée. En general, le parallelépipède fondamental de la roche est determiné par trois maxima; ainsi la distribution fondamentale des densités doit être construite par une superposition de 3 distributions du type indiqué en haut. C'est une fonction qui contient 11 paramètres, qui peuvent être déterminés par une minimisation fonctionnelle exécutée à l'aide d'un ordinateur. Dans cette façon, on obtient des limites de confiance.Afin de déterminer les contraintes régionales il ne faut que 2 maxima des pôles; ainsi le nombre de paramètres se reduit a 7. En conséquence de la théorie usuelle des épreuves, il faut 21 déterminations d'orientations des clivages dans un affleurement. Ainsi, la méthode paramétrique démontre qu'il ne faut la connaissance que de 21 clivages pour déterminer la direction des contraintes principales qui les ont produits. Si la dispersion de la distribution fondamentale est prise comme connue, ce nombre se reduit de plus à 15 environs, ce qui est à peu près le même nombre auquel on avait arrivé dans les considérations non-paramétriques.

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With 9 Figures