Fracture energy release and size effect in borehole breakout

The paper presents a simple approximate analytical solution of the remote stresses that cause the collapse of a borehole or other circular cylindrical cavity in an infinite elastic space. Regions of parallel equidistant splitting cracks are assumed to form on the sides of the cavity. Their boundary is assumed to be an ellipse of a growing horizontal axis, the other axis remaining equal to the borehole diameter. The slabs of rock between the splitting cracks are assumed to buckle as slender columns, and their post-critical stress is considered as the residual stress in the cracked rock. The buckling of these slab columns is assumed to be resisted not only by their elastic bending stiffness but also shear stresses produced on rough crack faces by relative shear displacements. The energy release from the infinite medium caused by the growth of the elliptical cracking region is evaluated according to Eschelby's theorem. This release is set equal to the energy dissipated by the formation of all the splitting cracks, which is calculated under the assumption of constant fracture energy. This yields the collapse stress as a function of the elastic moduli, fracture energy, ratio of the remote principal stresses, crack shear resistance characteristic and borehole diameter. The collapse stress as a function of crack spacing is found to have a minimum, and the correct crack spacing is determined from this minimum. For small enough diameters, the crack spacing increases as the (4/5)-power of the borehole diameter, while for large enough diameters a constant spacing is approached. In contrast to plastic solutions, the breakout stress exhibits a size effect, such that for small enough diameters the breakout stress decreases as the (? 2/5)-power of the borehole diameter, while for large enough diameters a constant limiting value is approached. Finally, some numerical estimates are given and the validity of various simplifying assumptions made is discussed.     

Radon variations in a Hungarian village

 A steady radon exhalation is assumed in most publications. In a village of North-East Hungary, however, high radon concentrations have been measured, differing strongly in neighbouring houses and varying in time, due to the interplay of geochemical phenomena. Received: 20 November 1995 · Accepted: 18 June 1996     

Solar flares: The gradual phase

One has to distinguish between two kinds of the gradual phase of flares: (1) a gradual phase during which no energy is released so that we see only cooling after the impulsive phase (a confined flare), and (2) a gradual phase during which energy release continues (a dynamic flare).The simplest case of (1) is a single-loop flare which might provide an excellent opportunity for the study of cooling processes in coronal loops. But most confined flares are far more complicated: they may consist of sets of unresolved elementary loops, of conglomerates of loops, or they form arcades the components of which may be excited sequentially. Accelerated particles as well as hot and cold plasma can be ejected from the flare site (coronal tongues, flaring arches, sprays, bright and dark surges) and these ejecta may cool more slowly than the source flare itself.However, the most important flares on the Sun are flares of type (2) in which a magnetic field opening is followed by subsequent reconnection of fieldlines that may continue for many hours after the impulsive phase. Therefore, the main attention in this review is paid to the gradual phase of this category of long-decay flares. The following items are discussed in particular: The wide energy range of dynamic flares: from eruptions of quiescent filaments to most powerful cosmic-ray flares. Energy release at the reconnection site and modelling of the reconnection process. The post-flare loops: evidence for reconnection; observations at different wavelengths; energy deposit in the chromosphere, chromospheric ablation, and velocity fields; loops in emission; shrinking loops; magnetic modelling. The gradual phase in X-rays and on radio waves. Post-flare X-ray arches: observations, interpretation, and modelling; relation to metric radio events and mass ejections, multiple-ribbon flares and anomalous events, hybrid events, possible relations between confined and dynamic flares.     

Some results of biogeographic research on meadows in the Dyje-Svratka basin in the Czech Republic

Some results of biogeographic research on meadows in the Dyje-Svratka basin in the Czech Republic. The paper shows one example of biogeographic inventory of natural ecosystems in an unflooded meadow in the Dyje-Svratka basin. It is part of the complex physio-geographic research of the Geographic Department of the Masaryk University in Brno aimed at gaining a basis for territorial interpretation of ecological regularities and territorial application of general ecological optimizing principles. A segment of biocenosis of Ulmi-fraxineta carpini has been analyzed (Zlatník 1956).The endeavour of Czech geographers to study geosystems of various dimensions completely gets in the limelight. In question is the understanding of mutual relationship of components of geosystems based on the exchange of mass and energy. There are two ways of studying them: spatial relations or approaches concentrated on processes. In contrast to the above unilateral concept, the endeavour to make the approaches compatible appears rarely. This complex view is made possible by geobiocenologically taken biogeography in papers of Zlatník and Rauer, their students and successors. This paper shows only one example of the results of biogeographic stock-taking of meadows in the Dyje-Svratka basin, indicating relations of eco- and geosystems which confirm the necessity of ecological orientation of the present biogeography and its potential contribution to ecology.     

Magnetic properties,self-reversal remanence and thermal alteration products of smythite

Summary This study is a follow up of the investigation of some magnetic properties and metastability of greigite in samples obtained from Miocene claystones in the Kruné hory (Erzgebirge) Piedmont basins (Bohemia). Three different methods of upgrading the smythite were applied; the magnetic properties of the concentrates are compared. The thermal conversion of smythite sets in at 200°C while greigite converts at 250°C. The first intermediate products to be formed are iron sulphides, marcasite clearly dominating over pyrite and pyrrhotite. Apart from a Fe³⁺ sulphate with a composition of Fe₂(SO₄)₃, oxidation of these sulphides gives rise to -Fe₂O₃. The result of the subsequent decomposition of the mentioned sulphate is the formation of -Fe₂O₃, which retains the sulphate structure. The final product of the thermal decomposition at 800°C is -Fe₂O₃. In the smythite concentrate the conversion to Fe³⁺ sulphate and -Fe₂O₃ is about twice as intensive as in greigite. No direct conversion to -Fe₂O₃ was found. During the thermal process self-reversals of remanence were observed, in various samples as many as four reversals in the temperature interval from 340 to 590°C. The occurrences of self-reversals of remanence were only observed at high degrees of thermal demagnetization, of the order of 10^–2 down to 10^–3 in the temperature interval of sulphide origin (below 400°C), and of the order of 10^–4 down to 10^–6 in the temperature interval of Fe-oxides origin (above 400°C).Presented at the 3rd Conference on New Trends in Geomagnetism, Castle of Smolenice, Czechoslovakia, June 22–29, 1992     

Fourier analysis of the light curves of eclipsing variables,II

The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.     

Quantification of mixing processes in ore-forming hydrothermal systems by combination of stable isotope and fluid inclusion analyses

In the Schwarzwald area, southwest Germany, more than 400 hydrothermal veins hosting different gangue and ore mineral assemblages cross-cut the crystalline basement rocks. Many of the post-Variscan fluorite-barite-quartz veins are considered to have precipitated through mixing of a deep saline brine with meteoric, low salinity waters. This hypothesis was tested using carbon, sulfur, and oxygen isotope data of sulfides, sulfates and calcite, coupled with fluid inclusion studies. Primary hydrothermal calcites from the deposits show a positive correlation of their δ¹³C (V-PDB) and δ¹⁸O (V-SMOW) values, which range from −12 to −3‰ and from 12 to 18.5‰, respectively. Carbon and oxygen isotope compositions of paragenetically young, remobilized calcite types are shifted towards higher values and range from −12 to −1‰ and from 20 to 25‰, respectively. We developed an improved calculation procedure for modeling the covariation of carbon and oxygen isotopes in calcite resulting from mixing of two fluids with different isotopic compositions and total carbon concentrations. In our model, the carbon speciation in the two model fluid end-members and the fluid mixtures are calculated using a speciation and reaction path code. The carbon and oxygen isotope covariation of primary Schwarzwald calcites can effectively be modeled by a mixing trend of a deep saline brine and a meteoric, low salinity water. Sulfur isotope data of barites from 44 hydrothermal fluorite-barite-quartz veins vary from 9 to 18‰ (CDT), sulfide ore minerals show δ³⁴S values between −14.4 and 2.9‰. Calculated sulfide-sulfate equilibrium temperatures are in the range between 300 and 350 °C. These temperatures differ significantly from the formation temperatures of 150 to 200 °C of most of the deposits as estimated from fluid inclusions, and are interpreted as preserved paleotemperatures of the deep aquifer. This assumption has been carefully checked against possible contamination of an equilibrated sulfide-sulfate system from the deep aquifer with sulfate from surface-derived sources, considering also the kinetics of the sulfide-sulfate isotope exchange. A combination of the S isotopic results with microthermometric fluid inclusion data and constraints on the temperature of the meteoric water was used to calculate mixing ratios of the two fluid end-members. The results indicate that mass fractions of the deep saline brine in the mixed fluid were between 0.5 and 0.75. Considering all geologic, geochemical and isotopic information, we propose that the majority of the post-Variscan hydrothermal veins in the Schwarzwald area were precipitated by district-scale mixing of a homogeneous deep saline brine with meteoric waters.