An improved Monte Carlo simulation method for discontinuity orientations based on Fisher distribution and its program implementation

Fisher distribution is the most commonly used probability density function for discontinuity orientations. Based on Fisher distribution, Monte Carlo simulation method for discontinuity orientations was reviewed and improved. Those orientations extending beyond the edge of an upper hemisphere projection (OEBEUHP) often have an important influence on both the mean orientation and Fisher constant K, thus affecting simulation results. The detailed algorithms for identifying and adjusting those OEBEUHP were developed in this paper. Based on the improved method, a program for generating discontinuity orientations and plotting their stereographic projection maps, named as MCSDO, was developed. Due to the aforementioned adjustment, the generated orientations by MCSDO are close to the original discontinuity orientations, which were mapped in field, and satisfactory. Only the original orientations and target number of generated orientations need to be input. By running the program we can directly obtain the follows: orientations of generated discontinuities, mean orientations of both original and generated discontinuities, Fisher constant K of both original and generated discontinuities, and stereographic projection maps of both original and generated discontinuities. MCSDO is a freeware designed for researchers and practicing engineers, and can be easily mastered with a little computer knowledge.     

节理岩体结构面产状的动态聚类分析

节理岩体结构面的优势产状是进行Mnote-carlo模拟和岩体稳定性分析的基础。玫瑰花图、等密度图等传统的图形分析方法比较粗糙,其结果只是相对的优势组数划分,无法准确地给出结构面的优势产状,使得分组结果在实际中应用不便。为弥补上述不足,采用改进的动态聚类分析方法,构造空间直角坐标系,以结构面的单位法向量表示其产状,并根据球面上两点之间的球面距离对结构面产状进行分类判定。将该方法应用于三峡库区巴东新县城铜盆溪桥东头高切坡结构面优势产状分析中。结果表明,采用改进动态聚类分析方法结果可靠,分类合理,可以较准确地确定结构面的优势产状。     

Wavelet Analysis and Filtering to Identify Dominant Orientations of Permeability Anisotropy

An accurate representation of permeability anisotropy is needed to model the rate and direction of groundwater flow correctly. We develop a wavelet analysis technique that can be used to characterize principal directions of anisotropy in both stationary and non-stationary permeability fields. Wavelet analysis involves the integral transform of a field using a wavelet as a kernel. The wavelet is shifted, scaled, and rotated to analyze different locations, sizes, and orientations of the field. The wavelet variance is used to identify scales and orientations that dominate the field. If the field is non-stationary, such that different zones of the field are characterized by different dominant scales or orientations, the wavelet variance can identify all dominant scales and orientations if they are distinct. If the dominant scales and orientations of different zones are similar, the wavelet variance identifies only the dominant scale and orientation of the primary zone. In this paper, we present a combined wavelet analysis and filtering approach to identify all dominant scales and orientations in a non-stationary permeability field. We apply the method to permeability data obtained in the laboratory from the Massillon sandstone.     

单轴拉伸条件下岩石本构理论研究

利用损伤力学理论研究了细观非均匀性岩石拉伸应力应变关系,包括:线弹性阶段、非线性强化阶段、应力降阶段、应变软化阶段。所用的模型分析了岩石的细观各向异性对全过程应力应变关系的影响,分析了产生应力跌落和应变软化的主要原因是损伤和变形局部化,将损伤和变形局部化引入本构模型是和以往模型的重要区别。通过与实验成果对比分析验证了模型的正确性和有效性。     

Measurement and correlation of microstructures: the case of foliation intersection axes

Recent studies have used the relative rotation axis of sigmoidal and spiral‐shaped inclusion trails, known as Foliation Inflexion/Intersection Axis (FIA), to investigate geological processes such as fold mechanisms and porphyroblast growth. The geological usefulness of this method depends upon the accurate measurement of FIA orientations and correct correlation of temporally related FIAs. This paper uses new data from the Canton Schist to assess the variation in FIA orientations within and between samples, and evaluates criteria for correlating FIAs. For the first time, an entire data set of FIA measurements is published, and data are presented in a way that reflects the variation in FIA orientations within individual samples and provides an indication of the reliability of the data. Analysis of 61 FIA trends determined from the Canton Schist indicate a minimum intrasample range in FIA orientations of 30°. Three competing models are presented for correlation of these FIAs, and each of the models employ different correlation criteria. Correlation of FIAs in Model 1 is based on relative timing and textural criteria, while Model 2 uses relative timing, orientation and patterns of changing FIA orientations, and Model 3 uses relative timing and FIA orientation as correlation criteria. Importantly, the three models differ in the spread of FIA orientations within individual sets, and the number of sets distinguished in the data. Relative timing is the most reliable criterion for correlation, followed by textural criteria and patterns of changing FIA orientations from core to rim of porphyroblasts. It is proposed that within a set of temporally related FIAs, the typical spread of orientations involves clustering of data in a 60° range, but outliers occur at other orientations including near‐normal to the peak distribution. Consequently, in populations of FIA data that contain a wide range of orientations, correlation on the basis of orientation is unreliable in the absence of additional criteria. The results of this study suggest that FIAs are best used as semiquantitative indicators of bulk trends rather than an exact measurement for the purpose of quantitative analyses.     

Comparative study of striations and basal till clast fabrics, Malpeque—Bedeque region, Prince Edward Island, Canada

Coastal erosion has resulted in exposure of a succession of basal till deposits and striation localities along the Malpeque and Bedeque Bays, PEI, Canada, permitting repetitive determinations of clast fabrics and investigation of recently exhumed striations. Striations indicate initial eastward ice flow, followed by a second glacial event with flow towards the south and southwest from the Gulf of St. Lawrence. The degree of local inconsistency and the variations with striation assemblages indicate that the orientations of individual striations cannot be regarded as 'absolute' indicators of ice flow directions. Diamictons identified as basal tills using sedimentological criteria have clast fabrics typical of basal till deposition. Local deviations of fabric trend within individual outcrops are common. A comparative analysis of the data obtained from striation and clast fabric orientations indicates that the ice flow directions independently suggested by each are in general agreement. Differences are present between the orientations of striations and clast fabrics at individual sites. The orientations of the fabrics lie within 20° of the modal striation orientations in only 28% of the cases, and the median deviation between the suggested ice flow directions was 29°. In 40%, of the cases, the azimuth deviation between the two methods exceeded 40°, and the maximum deviation recorded was 84°. At many sites, the deviations are so severe as to potentially result in the misinterpretation of the modal ice flow direction, based on the use of either striation orientation or clast fabric in isolation. Variations in glacial flow can readily produce striations and clast fabrics which record different phases of glacial activity associated with the same glacial event at an individual site.     

Progress in the study and modelling of similar fold interferences

Similar fold interferences are examined in two different ways.

• 1.(1) We show the importance of taking into account the original position of the stratification with respect to the orientations of two interfering fold phases. Basin and dome cases correspond to particular orientations of the interfering phases with respect to each other. In all other cases, coaxiality may be achieved for particular positions of the original stratification.
• 2.(2) We have achieved a computer-aided modelling which allows the visualization by means of sections and block-diagrams of any two or three similar fold interferences. The program allows us to define the stratification, orientations of the various phases and their profiles (sinusoidal or drawn by hand), and orientations and dimensions of the selected section or block diagram. Faults may also be represented.This modelling method is a powerful research tool that we hope to apply in future to detailed studies of fold interferences, to achieve quantitative field models of multiply folded and faulted terranes.

     

A mechanism for the development of en-echelon gashes in kink zones

Consistent arrangement of en-echelon gashes occurring within kink zones was observed and measured at several localities in the Lubec—Belleisle structural zone of southwestern New Brunswick.The special geometric relationship of both kinks and en-echelon fracture systems allow an interpretation of the regional and local stress orientations necessary to produce such combined features.Mohr-circle stress analysis of a modified direct shear model is used to postulate a mechanism whereby varying orientations of en-echelon tension gashes and boundary shears within kink zones can be explained. Using this analysis, the observed gash orientations can be generated by reduction in the local normal stress acting on original kink-zone boundaries, coupled with a corresponding increase in the normal stress acting transverse to such boundaries. These stress adjustments could be due to deflection of regional stress trajectories around local zones of yielding (by kinking) rock.     

Breakage assessment through cluster analysis of joint set orientations of exposed benches of opencast mines

Summary This paper substantiates, through three different case studies, that the breakage assessment of opencast bench blasting can be made scientifically through the analysis of joint set orientations of different exposed benches in association with the corresponding face direction. Joint orientations, dip and strike of bedding planes have a significant influence on rock breakage. They can have decelerating effects on blasting performance, which may be rectified by geological mapping, and subsequently modifying the blast design parameters.     

Recent intraplate stress field in the eastern Duero Basin (N Spain)

Palaeostresses inferred from brittle mesostructures in the eastern Duero Basin show a recent stress field characterized by an extensional regime, with local strike-slip and compressional stress states. Orientations of the maximum horizontal stress ( S_Hmax ) show a relative scattering with two main modes: NNE to NE–SW and NW–SE. These orientations suggest the existence of two stress sources responsible for the dominant directions of the maximum horizontal stress in northeastern Iberia. Extensional structures within a broad-scale compressional stress field can be related to both the decrease in relative stress magnitudes from active margins to intraplate regions and rifting proccesses ocurring in eastern Iberia. Stress states with NW–SE-trending S_Hmax are compatible with the dominant pattern established for western Europe. NE–SW orientations of S_Hmax suggest the occurrence of tectonic forces coming from the Pyrenean zone. Geological and geophysical data indicate the existence of both orientations from the upper Miocene to the present-day in NE Iberia.     

A comparison of Sanderson's and Panozzo's strain measurement methods using calcite grain boundaries from the Variscan fold and thrust belt in Ireland

Two methods of determining strain from the two-dimensional preferred orientation of lines by Sanderson and Panozzo are compared using grain boundaries in limestones from S Ireland. The Panozzo method utilizes the orientations and lengths of lines whereas the Sanderson method uses only the orientations. The Panozzo method is shown to be more sensitive to inhomogeneous deformation or dubious data than the simpler method of Sanderson.     

Origin of quartz clusters in Vinalhaven granite and porphyry,coastal Maine

We use the crystallographic orientations of quartz crystals, as determined with EBSD, to provide new evidence for the formation of clustered quartz crystals during magma crystallization. Vinalhaven is dominated by granite, with minor porphyry that formed when granite remelted during input of coeval basalt. CL zoning suggests that most quartz clusters in granite and porphyry formed by synneusis, the “swimming together” of preformed crystals. In granite, most quartz pairs in clusters have random orientations—only about 10% have parallel or Esterel twin orientations. Porphyry has fewer quartz clusters, and all pairs have approximately parallel or Esterel twin orientations. CL zoning of quartz pairs in porphyry indicates that they attached prior to a major remelting event. Interpretation of the Vinalhaven quartz clusters leads us to propose that oriented synneusis occurs during crystal accumulation on a magma chamber floor. During hindered settling, some quartz crystals should have come into contact along their dipyramidal faces. Once in contact, continued settling and loss of interstitial melt may have rotated some quartz crystals such that lattices on their dipyramidal faces matched—producing parallel and Esterel twin orientations and creating strong bonds between pairs. Only a small proportion of pairs with matched dipyramidal faces formed in the granite and, during rejuvenation to produce porphyry, only these oriented pairs survived. Hence, the presence of oriented synneusis in a plutonic rock may demonstrate a history of crystal accumulation.     

Crystallographic preferred orientation in albite samples deformed experimentally by dislocation and solution precipitation creep

The crystallographic preferred orientations of a series of experimentally deformed fine-grained albite aggregates were measured by synchrotron source X-ray diffraction. Most samples were deformed and extensively recrystallized by low-temperature recrystallization-accommodated dislocation creep. In axial compression as well as simple shear these samples developed weak but distinct crystallographic preferred orientations consistent with intracrystalline slip on {001}<100>; the sheared samples have a marked asymmetry of the <100> maxima with respect to the shear zone boundaries. One sample was axially compressed by solution precipitation creep; it developed a somewhat different but equally strong preferred orientation, perhaps reflecting crystallographic anisotropy in rates of dissolution and growth.     

Crystallographic orientations of high-angle grain boundaries in dynamically recrystallized quartz: First results

The crystallography and geometry of high-angle grain boundaries from dynamically recrystallized quartz have been studied. On the basis of combined electron backscatter diffraction and universal stage measurements, the complete crystallographic orientation of the grain boundaries could be calculated. The u-stage rotation of the grain boundaries to a vertical position reveals that they are never curved but always consist of straight segments. Our results show that these segments preferentially occupy rhombohedral, trapezohedral and bipyramidal orientations, i.e., orientations in a  25–50° girdle to the c-axis. A specific, albeit low, number of segments with special crystallographic orientation, with respect to a neighbouring quartz grain, often shows another special orientation with respect to the other neighbouring grain. Preferred combinations of grain boundary orientations related to both neighbouring grains are (i) low-index rhombohedral and high index trapezohedral, (ii) low-index bipyramidal and low-index trapezohedral or high-index rhombohedral, and (iii) low-index trapezohedral and low or high index trapezohedral. In certain cases, such as at triple junctions, the boundaries occupy specific trapezohedral orientations with a constant angle to the c-axis. This argues for energy isotropy of trapezohedral planes with the same angle to the quartz c-axis. In general, good match coincidence site lattice (CSL) orientations are not preferentially occupied so that most of the studied grain boundaries represent general boundaries. The formation of straight segments in special crystallographic orientations indicates the crystallographic control and implies an energy reduction of certain general boundaries.     

Fabric evolution in a numerical direct shear test

This paper presents a three-dimensional discrete element study on the mechanical behaviour and fabric changes of elongated particle assemblages in a direct shear test. Assemblages with elongated particles are prepared under different preparation methods: random placing and deposition. Particles are generated inside a direct shear box with arbitrary orientations in the random placing method. In the deposition approach, two directions of deposition are used: perpendicular and parallel to the shear direction. Assemblages formed by different methods give significantly different initial particle orientations. Different dilatancy responses and shear strengths are resulted upon shearing. Change in fabric along the shear plane is noticeable and the magnitude of such rotation depends highly on the initial particle orientation.     

The relationship between regional stress field,fracture orientation and depth of weathering and implications for groundwater prospecting in crystalline rocks

In a uniform granite gneiss study area in central Zimbabwe, lineaments oriented parallel to the maximum regional compressive stress orientation exhibit the thickest regolith development, while lineaments oriented perpendicular to the maximum compressive stress show the shallowest development of weathered regolith. The principal fracture set orientations were mapped using aerial imagery. The regional stress field, estimated from global stress maps, was used to determine the stresses acting on each principal lineament orientation. Multi-electrode resistivity profiling was carried out across fractures with different orientations to determine their subsurface regolith conditions. The results indicate that the 360 and 060° lineaments, which are sub-parallel to the principal compressive stress orientation (σ₁) exhibit maximum development of the regolith, while 130° lineaments perpendicular to σ₁ do not exhibit significant regolith development. Since regolith thickness has been positively correlated with groundwater resources, it is suggested that fractures with orientations sub-parallel to the principal compressive stress direction constitute favourable groundwater targets. Knowledge of the regional stress field and fracture set orientations can be used as an effective low cost tool for locating potentially higher yielding boreholes in crystalline rock terrains.     

Verification of a 3-D LiDAR Viewer for Discontinuity Orientations

Light detection and ranging (LiDAR) scanners are increasingly being used to measure discontinuity orientations on rock cuts to eliminate the bias and hazards of manual measurements which are also time consuming and somewhat subjective. Typically LiDAR data sets (point clouds) are analyzed by sophisticated algorithms that break down when conditions are not ideal, for example when some of the discontinuities are obscured by vegetation, or when significant portions of the rock face are composed of fractured facets, weathering generated surfaces, or anything that should not be identified as a discontinuity for the purposes of slope stability analysis. This paper presents a simple LiDAR point cloud viewer that allows the user to view the point cloud, identify discontinuities, pick three points on the surface (plane) of each discontinuity, and generate discontinuity orientations using the three-point method. Additionally, a test of our 3-D LiDAR viewer for discontinuity orientations on rock cuts in the United States of America and Canada is presented.     

Upper mantle anisotropy of southeast Arabia passive margin [Gulf of Aden northern conjugate margin], Oman

In this study, we used data recorded by two consecutive passive broadband deployments on the Gulf of Aden northern margin, Dhofar region, Sultanate of Oman. The objective of these deployments is to map the young eastern Gulf of Aden passive continental margin crust and upper mantle structure and rheology. In this study, we use shear-wave splitting analysis to map lateral variations of upper mantle anisotropy beneath the study area. In this study, we found splitting magnitudes to vary between 0.33 and 1.0 s delay times, averaging about 0.6 s for a total of 17 stations from both deployment periods. Results show distinct abrupt lateral anisotropy variation along the study area. Three anisotropy zones are identified: a western zone dominated by NW–SE anisotropy orientations, an eastern zone dominated with NE–SW anisotropy orientations, and central zone with mixed anisotropy orientations similar to the east and west zones. We interpret these shorter wavelength anisotropy zones to possibly represent fossil lithospheric mantle anisotropy. We postulate that the central anisotropy zone may be representing a Proterozoic suture zone that separates two terranes to the east and west of it. The anisotropy zones west and east were being used indicative of different terranes with different upper mantle anisotropy signatures.     

Temporal development of fabric in uniaxially stressed polycrystalline media—A theory

We present a kinetic theory for the development of lattice-preferred orientation in a uniaxiallystressed aggregate consisting of elastically uniaxial crystals. The fabric is brought about by grain-boundary migration alone; other fabric-producing mechanisms, such as plastic deformation, syntectonic recrystallization, and dissolution/reprecipitation, are specifically excluded from the theory. The formulation statistically averages the mass transfer between a typical crystal and its adjacent neighbors over all the possible crystallographic orientations of these neighbors and over all the possible orientations of the interfaces between the neighbors and the crystal of interest. The rate of mass exchange between two adjacent crystals is proportional (1) to the difference between chemical potentials and (2) to the surface area common to them. With these assumptions we find an equation for the massfraction density of crystals that have a given orientation (with respect to the stress) at any given time. The theory predicts that beyond a certain time a gap develops in the distribution of crystal orientations allowed: the only crystals that continue to exist are those for which the c-axis is within a certain, timedependent range about the stress.     

Fold-interference patterns in the Bowen Basin,northeastern Australia

Deformation patterns of Paleozoic and Mesozoic strata in eastern Australia are evidence of a structural and tectonic history that included multiple periods of deformation with variable strain intensities and orientations. Detailed analysis of structural data from the Bowen Basin in northeastern Australia reveals previously undescribed, north–south elongate, Type-1 fold-interference patterns. The Bowen Basin structures have similar orientations to previously described interference patterns of equivalent scale in upper Paleozoic strata of the New England Orogen and Sydney Basin of eastern Australia. The east Australian folds with north–south-trending axes most likely formed during late stages of the Permian–Triassic Hunter–Bowen Orogeny, and they were subsequently refolded around east–west axes during post 30 Ma collision of the Indo-Australian plate with the Eurasian and Pacific plates. The younger, east–west-trending folds have orientations that are well aligned with the present-day horizontal stress field of much of eastern Australia, raising the possibility that they are active structures.