True Spacing Research Articles

A New Analytical Solution for Calculating Rock Block Volume

The study of rock slope stability and evolution suffers from many uncertainty factors related to block size and shape, and slope morphology. While nothing can be done to remove the aleatory component of these uncertainties, efforts in reducing the epistemic ones are desirable. This research aims to propose a new analytical solution for calculating rock block volume in the case of three discontinuity sets whose orientation and true spacing are known. Researchers and practitioners can take advantage of such a correct analytical formula thanks to its easiness of use: guidelines based on stereogram are provided in order to explain how to obtain the required input data. The correctness of the equation is demonstrated by comparing the results of the new solution applied to 12 theoretical blocks with those obtained with 3DEC (Itasca Consulting Group). Also, the differences with respect to results obtained with the well-known Palmstrøm’s formula are reported. The new methodology is applied to the case study of Elva valley road (Northern Italy), which is overhung by steep rocky cliffs and is subject to the consequences of frequent rockfall phenomena. The results are used to discuss the proposed method’s applicability: while it is evident that such a formula is not able to compete with the great potentiality of DFNs, this user-friendly tool can quickly and at no cost assess rock block volume in rockfall or rock slope stability studies.

Characterization of discontinuities in potential reservoir rocks for geothermal applications in the Rhine-Ruhr metropolitan area (Germany)

Abstract. The importance of research into clean and renewable energy solutions has increased over the last decade. Geothermal energy provision is proven to meet both conditions. Therefore, conceptual models for deep geothermal applications were developed for different field sites regarding different local conditions. In Bavaria, Germany, geothermal applications were successfully carried out in carbonate horizons at depths of 4000 to 6000 m. Matrix permeability and thermal conductivity was mainly studied in karstified carbonates from the Late Jurassic reef facies. Similar to Bavaria, carbonates are located in the east of the Rhenohercynian Massif, in North Rhine-Westphalia (NRW), for which quantification of the geothermal potential is still lacking. Compared to Bavaria, a supraregional carbonate mountain belt is exposed at the Remscheid-Altena anticline (in NRW) from the Upper Devonian and Lower Carboniferous times. The aim of our study was to examine the potential geothermal reservoir by field and laboratory investigations. Therefore, three representative outcrops in Wuppertal, Hagen-Hohenlimburg, and Hönnetal were studied. During field surveys, 1068 discontinuities (139 open fractures without any filling, 213 joints, 413 veins filled with calcite, and 303 fractures filled with debris deposits) at various spatial scales were observed by scanline surveys. These discontinuities were characterized by trace length, true spacing, roughness, aperture, and filling materials. Discontinuity orientation analysis indicated three dominant strike orientations in NNW–SSE, NW–SE, and NE–SW directions within the target horizon of interest. This compacted limestone layer (Massenkalk) is approximately 150 m thick and located at 4000 to 6000 m depth, dipping northwards at a dip angle of about 30 to 40∘. An extrapolation of the measured layer orientation and dip suggests that the carbonate reservoir could hypothetically extend below Essen, Bochum, and Dortmund. Our combined analysis of the field and laboratory results has shown that it could be a naturally fractured carbonate reservoir. We evaluated the potential discontinuity network in the reservoir and its orientation with respect to the prevailing maximum horizontal stress before concluding with implications for fluid flow: we proposed focusing on prominent discontinuities striking NNW–SSE for upcoming geothermal applications, as these (1) are the most common, (2) strike in the direction of the main horizontal stress, (3) have a discontinuity permeability that significantly exceeds that of the reservoir rock matrix, and (4) only about 38 % of these discontinuities were observed with a calcite filling. The remaining discontinuities either showed no filling material or showed debris deposits, which we interpret as open at reservoir depth. Our results indicate that even higher permeability can be expected for karstified formations related to the reef facies and hydrothermal processes. Our compiled data set, consisting of laboratory and field measurements, may provide a good basis for 3D subsurface modelling and numerical prediction of fluid flow in the naturally fractured carbonate reservoir.

Determination of Engineering Geological Conditions of A Plant-Site: A Case Study in an Open Pit Mine in Çine, Aydın

A plant will be constructed between the Alipasa and Sarıkısık feldspar open-pit mines in Karpuzlu-Çine (Aydın) to conduct the works of crushing-grinding and flotation. An investigation was carried out to determine engineering geological conditions at and below the plant-site using scan-lines, geophysical measurements, and three inclined borehole data. Geological structure and ground conditions including geotechnical data such as discontinuity frequency and spacing, RQD% and CR% acquired from the drill hole exploration and geophysical survey are determined. Along the inclined drill holes, true discontinuity spacing values computed for each core run represent the most intersected discontinuities. In these calculations, determination of the acute angles between the axes of drill holes and strikes of the discontinuity sets are important as much as the investigation of fracture distributions in the subsurface. For this reason, the stereographic projection techniques were used to determine the true acute angle in this work. The purpose of the investigation is to identify and mitigate difficulties caused by ground conditions. The rock conditions comprise heavily jointed and weathered metamorphic rocks and the ability of these to support the foundations is considered. It was determined that the bearing capacity values obtained from the geotechnical computations considering RQD values agree with the ones acquired from the geophysical measurements, except the weakness zones (sheared zones). It was also determined that the values of allowable bearing pressure based on the geotechnical works are more conservative than the ones from the geophysical measurements. When all results are considered, the ratio between the allowable bearing capacity (qa) values acquired from geotechnical and geophysical measurements is close to 0.65.

Joint spacing distribution of granites in Hong Kong

The structural stability of rock masses is dictated by the inherent geological structures present, most notably joints. Joint spacings are one of crucial parameters to control the block volume, permeability, deformability as well as strength of rock masses. While extensive rock engineering projects have been carried out in Hong Kong in the last century, the distribution models of joint spacings in Hong Kong rocks have still rarely been studied systematically and published. This research examines true joint spacings of granites in fourteen different slope outcrops at various localities of Hong Kong. A total number of 1323 joint spacing measurements, belonging to 44 joint sets spanning from 0.005 m to 4.5 m, are obtained. The mean joint spacings among 44 joint sets studied are computed in a range of 0.11 m to 1.33 m. Lognormal Distribution is found to be the dominant joint spacing distribution of granites in Hong Kong. A further in-depth understanding of joint spacing distributions of Hong Kong granitic rocks, which covers about 35% of the total land area, is of profound practical value to the assessment of rock mass excavatability and numerical modelling of rock fracture network development.

Effect of interlamellar spacing on fracture toughness of nano-structured pearlite

Microstructural refinement to the nanoscale imparts tremendous strength to metals while following the Hall-Petch relationship. However, most manufacturing methods to make nanostructured metals are limited by the maximum size of the final product. Extremely fine pearlitic steels with mean true inter-lamellar spacing of 110nm and 63nm while having yield strength of 0.79GPa and 1.08GPa respectively have been produced by suitable alloying and appropriate undercooling to enhance the free energy available for transformation. The stronger pearlite shows enhanced plane strain fracture toughness thus offering a combination of high damage resistance and tolerance.

Determination of true null electrode spacing of an extrapolation chamber for x-ray dosimetry

An accurate determination of the true null distance between electrodes, that defines the sensitive volume of an extrapolation chamber, is critical for the establishment of a primary measurement method for absorbed dose in tissue. In this work, a critical analysis of two methodologies for determining the true null electrode spacing of a 23392 Böhm model PTW extrapolation chamber was done.

Controlled spacing of self-organized anodic TiO2 nanotubes

We report on how to grow and control self-organized TiO2 nanotube arrays that show defined and regular gaps between individual nanotubes. For this we use electrochemical anodization of titanium in fluoride containing di-ethylene glycol (DEG) electrolytes, with variations in voltage and water content in the electrolyte. In these specific electrolytes, such nanotubes show a true spacing, i.e. nanotubes are spaced both at top and at bottom in regular intervals, this in contrast to classic nanotubes obtained in other organic electrolytes showing a close-packed organization. We identify critical parameters that define the “region of existence” i.e. under which condition tube spacing occurs as well as the intertube distance, to be the voltage and the water content. Using these findings allows to grow tubes where diameter and spacing can even be independently controlled.

Evolutionary Multi-objective Optimization in Building Retrofit Planning Problem

Energy efficiency has been a primary subject of concern in the building sector, which consumes the largest portion of the world's total energy. Especially for existing buildings, retrofitting has been regarded as the most feasible and cost-effective method to improve energy efficiency. When planning retrofit in public buildings, the most obvious objectives are to: (1) minimize energy consumption; (2) minimize CO2 emissions; (3) minimize retrofit costs; and (4) maximize thermal comfort; and one must consider these concerns together. The aim of this study is to apply evolutionary multi-objective optimization algorithm (NSGA-III) that can handle four objectives at a time to the application of building retrofit planning. A brief description of the algorithm is given, and the algorithm is examined using a building retrofit project, as a case study. The performance of the algorithm is evaluated using three measures: average distance to true Pareto-optimal front, hypervolume, and spacing. The results show that this study could be used to find a comprehensive set of trade-off scenarios for all possible retrofits, thereby providing references for building retrofit planners. These decision makers can then select the optimal retrofit strategy to satisfy stakeholders’ preferences.

Stability of a Lamellar Structure – Effect of the True Interlamellar Spacing on the Durability of a Pearlite Colony / Stabilność Struktury Płytkowej – Wpływ Rzeczywistej Odległości Międzypłytkowej Na Trwałość Kolonii Perlitu

A lamellar microstructure is, beside a granular and dispersive one, the most frequently observed microstructure in the case of metal alloys. The most well-known lamellar microstructure is pearlite, a product of a eutectoidal transformation in the Fe-Fe3C system. The lamellar morphology of pearlite - cementite and ferrite lamellae placed interchangeably within one structural unit described as a colony - is dominant. The durability of the lamellar morphology is much diversified: in the microstructure of spheroidizingly annealed samples, one can observe areas in which the cementite is thoroughly spheroidized, next to very well-preserved cementite lamellae or even whole colonies of lamellar pearlite. The mentioned situation is observed even after long annealing times. The causes of such behaviour can vary. The subject of the previous work of the authors was the effect of the orientation between the ferrite and the cementite on the stability of the lamellar morphology. This work constitutes a continuation of the mentioned paper and it concerns the effect of the true interlamellar spacing on the stability of the lamellar morphology of cementite.

SOME ASPECTS OF ESTIMATION ACCURACY OF MEAN TRUE INTERLLAMELAR SPACING

Lamellar microstructures are characterized by interlamellar spacings: random, apparent and true. The mean value of true interlamellar spacing can be estimated by measurements of apparent spacings, random spacings or by counting number of intersections the secant with plates. In this paper the statistical errors in true interlamellar spacing measurements has been determined and discussed using the example of pearlite in eutectoid steel. The accuracy of estimation of true interlamellar spacing using all the methods is comparable and sufficient.

Experimental study of lattice distortion in ellipsoid-like nano-crystallites of copper

The elastic state of embedded inclusions is of considerable importance to the properties of materials. The non-uniform lattice distortion in the inclusions in which the interfaces are shaped with variable curvature cannot be measured by usual experimental methods. In this paper, the lattice distortions in an ellipsoid-like nano-crystallite of copper were measured by means of the peak finding method in the central part of the HRTEM image. The effects of contrast delocalization are studied by HRTEM image simulations, which show that the measured spacings of peaks in the middle part of the crystallite can be considered approximately equal to the true spacings of columns. With the HRTEM method, our measured results show that the nano-crystallite is expanded in the short axis direction and compressed in the long axis direction. The results calculated with the elasticity theory incorporating interface tension consist with the experimental results of HRTEM.

Application of the Disector to Determine the Distribution of True Interlamellar Spacing in Lamellar Microstructures

Abstract It is well known that the interlamellar spacing controls the mechanical properties of any material with a lamellar microstructure. It is also expected, although not yet established, that varying distribution of interlamellar spacing would also influence the properties. However, the problem of determining the distribution of interlamellar spacing from metallographic observations made on single 2D sections is almost intractable. A technique to estimate the true interlamellar spacing in a lamellar microstructure, using a 3D probe referred to as a disector, has been developed. This disector technique was used to obtain the distribution of true interlamellar spacing of pearlite in a microalloyed steel. The results indicate clearly that there is a significant variation of interlamellar spacing across pearlite colonies and also within individual colonies. In addition, it was possible to determine the overall distribution of interlamellar spacing.

Interlamellar Spacing of Pearlite in a Near-eutectoid Fe–C Alloy Measured by Serial Sectioning

The interlamellar spacings of pearlite formed isothermally at 700 and 680°C in a near-eutectoid Fe–0.82mass%C alloy were measured by serial sectioning coupled with scanning electron and atomic force microscopy. The intersection angle of cememtite lamellae with the metallographic surface was determined from the variation of horizontal displacement of cementite lamellae with removal depth. The true lamellar spacing was then calculated from the apparent lamellar spacing on the surface. When the angle was small, i.e. less than ~20°, it was measured directly by atomic force microscope. The minimum and mean true lamellar spacings are in good agreement with those measured by other methods. The distribution of interlamellar spacings on the specimen surface back calculated from the spectra of true interlamellar spacing assuming the random orientation of cementite lamellae was in fair agreement with the measured one. It is likely that the distribution of true lamellar spacings is primarily due to recalescence and the minimum true spacings rather than the mean value may be relevant to the thermodynamic theory of pearlite transformation.

Evaluation of true interlamellar spacing from microstructural observations

A method for evaluating true interlamellar spacing from micrographs is proposed for a multidomained lamellar structure. The microstructure of these materials is assumed to be composed of many domains with the lamellae aligned roughly parallel to each other within each domain and with the domains themselves randomly oriented relative to one another. An explicit expression for the distribution of apparent interlamellar spacing is derived assuming that the distribution of the true interlamellar spacing is Gaussian. The average interlamellar spacing is close to the peak interlamellar spacing observed in the distribution. The theoretical distributions are compared with experimental ones obtained by analyzing micrographs of PbTe–Sb2Te3 lamellar composites.

Granite fracture index to check suitability of granite outcrops for quarrying

A correct knowledge of fracture patterns previous to quarrying is important for economical exploitation. This work comprises the general characterization of the discontinuities of 10 granite rock masses in NE Portugal. During the study some discontinuity characteristics such as orientation, persistence, aperture, trace length and spacing were evaluated. The differences in the characteristics of the selected granites were described, and the most important exploration factors were identified. In the granites studied, most of the joints are oriented from N10°E to N50°E, which is compatible with the regional fracture pattern. Concerning joint termination, the XX type is common, while the RR type is rare; the persistence index ranges from 3.5% to 25.4%. Closed joints are predominant in the granites studied (> 72.4%), and openings of the others are about 1–2 mm as a result of superficial displacement of the granite blocks. The percentage of filled joints, usually by quartz and pegmatite, is different from one granite to another, but most are < 20%. The average joint length ranges from 11.1 m in post-tectonics granites to 4.6 m in syntectonic granites. Joint spacing varies from 0.98 to 2.8 m with higher values in post-tectonic granites. Joint-space distributions of the granites studied are close to log-normal and exponential distributions. Volumetric joint count (Jv) ranges from 0.8 to 2.1 joints/m 3 and is used for categorizing the places of each granite. The relationships between Jv and other joint characteristics, such as length, spacing and number of joint sets, were investigated. A Granite Fracturing Index (GFI) is introduced, computed on the basis of volumetric joint count, number of joint sets and true joint spacing. The GFI classification of studied places allows us evaluate the suitability for profitable exploitation.

A three-dimensional analysis of the development of the horizontal cell mosaic in the rat retina: Implications for the mechanisms controlling pattern formation

The horizontal cells are known to form a mono-layered mosaic in the adult retina, but are scattered at different retinal depths in early development. To help clarifying when and which spatial constraints appear in the relative positioning of these cells, we have performed a quantitative analysis of the three-dimensional (3D) organization of the horizontal cell mosaic at different developmental stages in the postnatal rat retina. We first analyzed the two-dimensional (2D) distribution of the horizontal cell projections onto a plane parallel to the upper retinal surface in retinal flat-mounts, and thus to the future mature horizontal cell mosaic. We found that this 2D distribution was non random since postnatal day 1 (P1), and had a subsequent stepwise improvement in regularity. This preceded the alignment of cells in a single monolayer, which was observed on P6. We then computed true horizontal cell spacing in 3D, finding non-random 3D positioning already on P1. Simulation studies showed that this order might simply derive from the 2D order observed in the projections of the cells in flat-mount, combined with their limited spread in retinal depth. Throughout the period analyzed, the relative positions of horizontal cells are in good agreement with a minimal spacing rule in which the exclusion zone corresponds to the average size of the inner core of the cell dendritic tree estimated from P1 samples. These data indicate the existence of different phases in the process of horizontal cell 3D spatial ordering, supporting the view that multiple mechanisms are involved in the development of the horizontal cell mosaic.

The effect of limited lateral resolution in the measurement of implant surface roughness: A computer simulation

The surface roughness of dental implants affects the bone response elicited. Surface roughness is generally described by a range of surface texture parameters. The aim of the present study was to use computerized simulation to investigate the extent to which the lateral resolution of an instrument/method limits the accuracy of certain surface roughness parameters. The lateral resolution was defined as the pixel size of a profiling system. A surface roughness was simulated by a trigonometric function with random periodicity and amplitude. The function was divided into an array of pixels simulating the pixels of the profiling system. The mean height value for each pixel was used to calculate the surface roughness parameters. It was found that the accuracy of all the surface roughness parameters investigated decreased with increasing pixel size. This tendency was most pronounced for mean slope and developed length ratio; amounting to about 80% of their true values for a pixel size of 20% of the true mean high-spot spacing. It was concluded that the lateral resolution of an instrument/method severely compromises the precision of surface roughness parameters measured for roughness features with a mean high-spot spacing less than five times the lateral resolution.

Nonstationary Kalman Filter for Estimation of Accurate and Consistent Car-Following Data

Difficulty in obtaining accurate car-following data has traditionally been regarded as a considerable drawback in understanding real phenomena and has affected the development and validation of traffic microsimulation models. Recent advancements in digital technology have opened up new horizons in the conduct of research in this field. Despite the high degrees of precision of these techniques, estimation of time series data of speeds and accelerations from positions with the required accuracy is still a demanding task. The core of the problem is filtering the noisy trajectory data for each vehicle without altering platoon data consistency; i.e., the speeds and accelerations of following vehicles must be estimated so that the resulting intervehicle spacings are equal to the real one. Otherwise, negative spacings can also easily occur. The task was achieved in this study by considering vehicles of a platoon as a sole dynamic system and reducing several estimation problems to a single consistent one. This process was accomplished by means of a nonstationary Kalman filter that used measurements and time-varying error information from differential Global Positioning System devices. The Kalman filter was fruitfully applied here to estimation of the speed of the whole platoon by including intervehicle spacings as additional measurements (assumed to be reference measurements). The closed solution of an optimization problem that ensures strict observation of the true intervehicle spacings concludes the estimation process. The stationary counterpart of the devised filter is suitable for application to position data, regardless of the data collection technique used, e.g., video cameras.

Effect of carbon concentration on tensile behaviour of pearlitic steels

A quantitative relationship between flow stress and microstructure is studied for pearlitic steels incorporating 0.39 - 0.77 wt-% carbon. The distribution of true lamellar spacing (S0) is determined. It is found that S0 depends on carbon concentration and pearlite transformation temperature accompanying a considerable distribution. The 0.2% proof stress is described as a function of the averaged S0 but the influence of the accuracy in S 0 measurement precludes satisfactory prediction of the 0.2% proof stress. High work hardening corresponds to the generation of phase stress caused by misfit plastic strain between ferrite and cementite. The stress partitioning behaviour between ferrite and cementite is verified by in situ neutron diffraction during tensile deformation.

Level correlation in coupled harmonic oscillator systems

From the viewpoint of nearest neighbour energy levels statistics, harmonic oscillator systems are unusual. Although it is integrable but does not follow the generic rule and the precise form of p( s) distribution depends on the arithmetic nature of the irrational frequency ratios. So from the old studies in this direction no deterministic conclusions have been gained so far and it needs further study in some new direction for its complete resolution. Spectral rigidity is often used as a stronger tool than the p( s) distribution as it can easily take account of long range correlations. Here we present correlation between levels in both small and large energy scale for coupled and uncoupled 2D HO. Instead of true level spacings we use scaled level spacings and our numerical results nicely show that in HO systems energy levels are highly correlated, regular and very rigid.