Probabilistic modelling of joint orientation

Observed frequencies of joint orientations are subject to error due to sampling bias. This error should be corrected before statistical inference is made on the distribution of orientation. Corrections (weighting functions) are developed for sampling bias in orientation for finite joints of different sizes and shapes intersecting rectangular exposures. Chi-square goodness-of-fit procedures available for hemispherical normal and bivariate normal distributions are modified to make them applicable for both raw data and data corrected for sampling bias. The aforementioned corrections and procedures were applied to a joint orientation cluster to study the effect of (a) joint orientation, (b) joint size and (c) joint shape, on the statistical distribution of the orientation. The influences of all these aforementioned factors were found to be significant. However, at present, joint sizes and shapes are not measured in field joint surveys. Therefore, it is suggested to make attempts to obtain joint sizes and shapes in field joint mapping surveys. Since the currently available probability distributions are not adequate to represent all joint orientation distributions, it is suggested either to look for new probability distributions or to develop procedures to use empirical distributions in modelling orientation distributions.     

Effects of joint orientation and rock mass quality on tunnel blasting

It is a well known fact that rock mass properties influence the process of fragmentation considerably. Model blasts and field investigations were carried out to find the effects of rock mass quality and joint orientation on tunnel blasting. Propagation of shock waves are partially restricted by joint planes. It was observed that the blast results (i.e., average fragment size and depth and cross-sectional area of the broken zone) were considerably influenced by joint orientation. Accordingly, it has been concluded that loading equipment with a larger capacity and deeper blast holes are required in formations with joint planes perpendicular to the tunnel axis. The number of blast holes, however, should be greater when joints are parallel to the tunnel axis. Furthermore, the powder factor (kg/m³) has been found to be directly related to rock mass quality (Q). Optimisation of pull, powder factor and overbreak is required in the case of weak formations with joints perpendicular to the tunnel axis. The use of contour blasting technique seems to be essential in poor and fair rock masses to minimise the overbreak, reduce the support cost and improve the stability of the opening.     

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.     

Maximum likelihood estimation of joint size from trace length measurements

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.     

On the orientation of tensile dikes in a ridge-centered plume

We present three-dimensional numerical models of the ascent of a plume under a spreading ridge and the concomitant melt generation and crust formation using a mantle viscosity which depends on pressure, temperature, melt content, and, optionally, water content. From the velocity field of these convection models we compute the viscous stress tensor in the mantle. Assuming that melt-rich channels or melt-filled dikes are oriented parallel to the maximum compressional stress, we calculate the orientation of such dikes in the partially molten zone of the plume head and beneath the ridge. For the central part of the plume we find dike orientations parallel to the ridge in shallow parts of the plume head, while they are ridge-perpendicular at greater depth. The boundary between these two regimes is shifted downwards for a water-rich plume which dehydrates upon melting. The two regimes of different dike or melt channel orientations seem to be in good agreement with seismic observations on depth-dependent seismic anisotropy, indicating a preference of our wet model. We find a modest focusing of melt towards the spreading center beneath normal ridge in both models, but also in the fully dehydrated parts of the plume head in the model where water was included; those are regions where upwelling is essentially passive. In contrast, the plume in the water-free model and the only partly dehydrated parts of the plume in the water-bearing model tend to develop a dike orientation which moves melt away from the spreading center; these regions are characterized by active upwelling. The defocusing of melt in actively upwelling plume mantle has radial symmetry about the plume axis, i.e. an outward orientation of the dikes is not only visible in planes perpendicular to the ridge, but also along the ridge.     

灰色关联度分析法在土地评价中的应用

作者选取四川省“金土工程”数据库中的原始数据作为研究基础，通过应用灰色系统理论的关联分析方法，以坡度、地面岩石露头、灌溉保证、排水条件、土壤构型、有效土层厚度、土壤酸碱度和土壤有机质作为与水稻平均产量相关的因子进行多因素关联分析，结果显示该区域排水条件与其产量具有最大的关联度。这说明在四川地区水稻地排水条件的优劣最大程度地决定着水稻的产量。通过各要素权重值的计算得到该地区土地等级划分范围。表明在土地评价中运用灰色关联度分析方法可减少人为的经验误差，同时该方法简单易行，结果可信度商。     

Correlation between joint orientation and geophysical stresses in a test area on the Canadian Shield

SummaryCorrelation Between Joint Orientation and Geophysical Stresses in a Test Area on the Canadian Shield It is contended that the orientation of the geophysical stress field in an area can be deduced from an analysis of the orientation of the joints which it has produced. As a test area, a reasonably homogeneous region of the Canadian Shield in the vicinity of Three-Mile-Lake in Ontario (roughly lat. 45° 10N and longitude 79° 25W) was chosen for analysis. It was found that the stresses were indeed homogeneous over an area of about 10 × 4 km with the exception of a small area which also shows petrographic and geomorphic peculiarities. Thus, local tectonic anomalies can immediately be recognized in the joint patterns.

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ZusammenfassungKorrelation zwischen der Lage von Klüften und dem geophysikalischen Spannungsfeld in einem Testgebiet im kanadischen Schild Es wird die Hypothese aufgestellt, daß die Hauptachsenrichtungen des geophysikalischen Spannungsfeldes aus der Lage der von ihm verursachten Klüfte abgeleitet werden kann. Um die Hypothese zu prüfen, wurde ein verhältnismäßig homogenes Gebiet des kanadischen Schildes in der Nähe vom Three-Mile-See in Ontario (ungefähr 45° 10N Breite und 79° 25W Länge) ausgewählt. Es wurde festgestellt, daß das abgeleitete Spannungsfeld über ein Gebiet von 40 km² tatsächlich homogen ist, mit Ausnahme einer kleinen Fläche, welche auch petrographische und geomorphologische Anomalien aufweist. Es können daher tektonische Anomalien sofort in den Klüftediagrammen erkannt werden.

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RésuméCorrelation entre l'orientation des clivages et les contraintes tectoniques dans une région d'épreuve du bouclier Canadien L'hypothèse est maintenue que l'orientation du champ des contraintes tectoniques peut être déduite par une analyse de l'orientation des clivages qu'il a produite. Comme région d'épreuve, une région à peu près homogène du bouclier Canadien dans le voisinage du Lac-des-Trois-Miles (45° 10N, 79° 25W) a été choisie. Il est démontré que les contraintes sont actuellement homogènes dans une région de 40 km², y exceptée une petite région où l'on observe aussi des péculiarités pétrographiques et géomorphologiques. Ainsi, les anomalies tectoniques locales peuvent être reconnues immédiatement dans les dessins du clivage.

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With 14 Figures     

Applicability of the theory of hollow inclusions for overcoring stress measurements in rock

Summary Whenever solid or hollow inclusions are used as instrumented probes in overcoring techniques, residual stresses remain in the overcored rock sample and in the probes. When using such devices for computing the in-situ stress field components from measured strains or displacements, it is common practice to assume that the overcoring diameter is infinite and that there is a perfect bonding between the rock and the probes. The validity of these assumptions depends on the magnitude of the residual stresses at the rock-probe contact as compared to the tensile and shear strengths of the rock-probe bond material. It also depends on the distribution of residual stresses in the overcored sample.In comparison to previous work, new expressions are proposed in this paper for the residual stresses associated with solid or hollow inclusion type stress probes in anisotropic ground. These expressions are presented in dimensionless form and are used to show that the distribution and magnitude of residual stresses depend on the isotropic-anisotropic rock character, the degree and type of rock anisotropy, the orientation of the rock anisotropy with respect to the hole in which the probes are located and the relative deformability of the rock with respect to the deformability of the material comprising the probes. The conditions that are required for neglecting the overcored sample diameter are also discussed. This is shown for rocks that can be described as isotropic, transversely isotropic and orthotropic materials.     

A critical evaluation of the available measurements for the stable isotopes of boron

The reported measurements for the stable isotopes of B (¹¹B and ¹⁰B) in natural materials are compiled, critically reviewed and evaluated. The selected values along with a discussion of the error, indicate the potential exists for using B isotopes in interpreting geochemical environments. The isotopic values for δ¹¹B range from -31%₀ for terrestrial rocks to +40%₀ for sea water, relative to NBS SRM-951 which has a reported ¹¹B/¹⁰B ratio of 4.04362 ± 0.00137 (2σ). Furtherm the isotope ratios generally form a narrow cluster of values for specific rock types. In some instances the reported δ¹¹B may be shifted substantially from the mean of “unaltered” rock as a result of weathering or reaction such as the progressive enrichment of δ¹¹B in marine sediments over time due to reaction with sea water.An application of widespread interest is the use of B isotopes in environmental studies. Boron is a contaminant derived from numerous sources such as municipal and industrial waste. The δ¹¹B in these wastes or processed waters is often significantly different from the δ¹¹B of the local ground-water, which will likely reflect the δ¹¹B values of the nearby rocks. This modification by contaminated water can be >20%₀ different from the δ¹¹B of the unaffected water, providing a useful tool in delineating the source of contamination and the direction of migration.     

Development of preferred orientation in plane strain deformed limestone: Experiment and theory

Carbonate rocks deform preferentially by twin gliding on e={01ˉ18} and slip on r ={10ˉ14} and f={02ˉ21}. In polycrystalline aggregates strong textures develop. We report on experimentally produced textures in triaxial plane strain geometry with orthorhombic symmetry at 200° C and 400° C. Pole figure of the experimentally deformed specimens are compared quantitatively with theoretical simulations based on the Taylor theory using both slip and mechanical twinning as mechanisms. Agreement at low and high temperature is satisfactory and documents that models developed for f.c.c. metals can be applied to low symmetry minerals provided that deformation mechanisms are known and that mechanical twinning is properly accounted for. Comparison with experimental results indicates that strain was nearly homogeneous at the conditions considered and the same may apply to many geological textures. Three texture types are described which are differentiated mainly by the relative importance of e twinning.     

On the method of spiral arms monotony to determine the orientation angles of galaxies

A method is proposed for the determination of the position and inclination angles of the plane of a spiral galaxy based on the assumption that every spiral arm is a monotonic function of the radius and/or the azimuthal angle. This method may yield more accurate results than the more commonly employed isophote method, which is fraught with various drawbacks. The use of the new method is illustrated by applying it to a sample of 43 objects, and the results agree well with data from other sources.     

The determination of joint directions by seismic refraction measurements at the Avedat plateau (Israel)

A seismic refraction experiment was conducted in an area at a site where joints had been mapped in detail in order to determine whether velocity anisotropy could be correlated with joint directions. The purpose was to assess the possibility of using seismic refraction techniques for mapping joint directions in alluvium-covered areas.The results of the experiment show that a velocity anisotropy can be detected by simple seismic refraction measurements, and that the anisotropy can be correlated with the dominant joints. It is believed that the technique is applicable to the determination of joint directions in alluvium-covered areas.     

On the accuracy of the theory of precession and nutation

Corrections to the IAU 2000/2006 parameters of the theory of precession and nutation are calculated using five different series—two individual series and three combined series that have been used in the literature for this purpose. A comparison of the sets of corrections obtained using the different datasets indicates significance systematic differences between them, which often substantially exceed the corresponding random errors. At the same time, existing studies have usually used data obtained from one or two series chosen by the authors without special justification. When refining the theory of precession and nutation, it is necessary to consider and compare various available series of VLBI data if one wishes to reduce the systematic errors in an improved model.     

Vulnerability of existing buildings: empirical evaluation and experimental measurements

The aim of this study is the comparison between the fundamental periods identified experimentally and those calculated using the formulas given in the Algerian Seismic Code (RPA 99) for vulnerability assessment and for experimental data collection of selected sample of old buildings. The results obtained for vulnerability assessment will then be extrapolated to buildings of the same typology built during the 1949 to 1954 period in the northern part of Algeria. From 1949 to 1954, the reinforced concrete constructions in Algeria were built before the first generation of the Algerian Seismic Code. These buildings being old are certainly weakened by the occupancy activities and seismic event loads. Hence, the evaluation of their vulnerability with respect to the regional seismic hazard requires the knowledge of their structure on a site capacity. The empirical formulas to calculate the fundamental period of a building are based on the Algerian Earthquake Code (RPA 99) .These formulas consider only the geometrical dimension (length, width and height) and the structural design of the buildings. The fundamental periods of vibration of twenty-two buildings, located in Algiers, calculated using the empirical formulas given in the RPA 99 are lower than those identified experimentally. A question then rises, do these tested buildings present any damage or not? As five of these buildings were tested before the 21 May 2003 earthquake, the experimental testing highlighted a decrease in the fundamental frequency which means that these buildings are damaged. Hence, for vulnerability assessment, the empirical formulas given in the Algerian Seismic Code (RPA 99) may not be appropriate for vulnerability assessment of the old buildings built during the 1949 to 1954 period.     

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.     

基于多重分形特征的岩体结构面剪切强度研究

Barton剪切强度模型是目前工程实践中普遍采用的强度公式,而实践应用时,该模型中结构面粗糙性系数（JRC）的评估存在主观性和片面性的缺点。鉴于此,应用多重分形理论,提出了采用多重分形参数准确量化JRC的方法。首先应用数字图像处理技术获取了结构面三维形貌数据信息;然后采用投影覆盖法进行了结构面的分形维数计算,重点对结构面的多重分形特征进行了分析,通过对比分析了构造的15个结构面的多重分形特征值。结果表明：结构面越粗糙,多重分形特征参数 和 值越大, 或 能够很好地描述结构面的形貌特征。最后对9组石膏试件进行了剪切试验,通过不同正应力下对应的剪应力数据分析,结合结构面形貌多重分形参数 或 ,以Barton剪切强度公式为基础,应用最小二乘法原理,给出了JRC与 及JRC与 关系。这样在工程实际中,可以用参数 或 对JRC进行估算,克服了JRC人为估值主观性及采用二维标准轮廓线评估片面性的缺点,为准确评估结构面粗糙度提供了一条新的途径。在此基础上,应用Barton模型可准确估算岩体结构面的剪切强度。     

On the geobiological evaluation of hydrocarbon source rocks

Hydrocarbon source rocks are characterized by the hydrocarbon discharge, and the alteration and variation in organic compositions and organic content due to the enhanced thermal maturation. These variations throw constraints on the application of the conventional inversion evaluation of hydrocarbon potential by assessing the residual organic matter left in source rocks. Geobiology, probing the interaction between the life system and the earth system, provides new principles in deciphering the whole dynamic processes related to the organic evolution history from living biomass to organic burial. Geobiological subdisciplines, including molecular geobiology, geomicrobiology, geoecology and biogeochemistry, offer new methodology and techniques to estimate the paleoproductivity, depositional organics and organic burial capacity and their components. Geobiofacies, newly proposed herein, is terminologized to define the geobiological dynamic processes through the combination of biofacies with organic facies and sedimentary facies, and expressed by the biohabitat types, paleoproductivity, depositional and preserved organics. Geobiofacies is identified as a useful means to create the geobiological evaluation system, which in turn rectifies the conventional evaluation system for the marine source rocks. __________ Translated from Earth Science—Journal of China University of Geosciences, 2007, 32(6): 727–740 [译自: 地球科学—中国地质大学学报]     

中国热液铀矿成矿理论体系

在总结前人大量研究成果的基础上,笔者尝试对我国的热液铀矿成矿理论体系作一简要概括。在成矿的＂源-运-导-集-存＂基本规律问题上,此体系大体包含以下10个方面：（1）硅化带成矿类型;（2）矿-岩时差;（3）碱交代作用;（4）成矿壳层;（5）4种铀矿类型（花岗岩型、火山岩型、碳硅泥岩型、砂岩型）统一构造-热液成矿;（6）铀成矿预富集序列;（7）花岗岩岩浆演化链的解耦;（8）绢英岩化高温富矿类型;（9）玄武岩事件;（10）幔汁成岩成矿论。     

On the theory of Al,Si ordering in albite

Calculations of the equilibrium distribution of Al, Si in the albite framework based on quasi-chemical theories of order, disorder transformations (Yang 1945; Yang and Li 1947; Li 1949) were made for a two-dimensional framework model. The ordering is caused by the energy of Al, Si interchange between sites of different crystal-chemical types and the energy of nearest neighbour interaction. By taking into account the decrease in the energy of interchange between sites with increasing disordering and with increasing temperature, and by examining different relationships for site-to-site interchange energy and the nearest neighbour interaction, it is possible to understand the basic characteristics of the transformation from low (essentially ordered) to high (essentially disordered) albite as revealed by experiment. These characteristics are: (1) abrupt variation of the equilibrium degree of order within a narrow temperature range and possible first order phase transformation for the transition from low-albite to high-albite, (2) hysteresis of the synthetic high albite transformation path and of the low albite hydrothermal “annealing” path, (3) presence of a temperature range where high albite is stable and has a continually changing equilibrium degree of order.     

On the least-squares fit of small and great circles to spherically projected orientation data

Given the direction cosines a _i ^′ = (a ₁ ⁱ , a ₂ ⁱ , a ₃ ⁱ )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x₁, x₂, x₃, x₄)for the angular radius x₄,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking x_j+1 = x_j + Δxwhere x_j is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.