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.     

Anwendungsmöglichkeiten der Guinier-Kamera nach v. Wolff bei der röntgenographischen Tonuntersuchung

Ohne Zusammenfassung     

X-ray determination of brushite (CaHPO4 · 2H2O) suspended in the water of the Neckar River,west Germany

The results reported in the present paper are a by-product of a detailed study of the heavy metals (Zn, Pb, Cu, Cd, Co, Ni, Cr, Fe, Mn) carried by the Upper Neckar River, Germany. The purpose was to determine the pollution by industrial waste of the river waters (Abadian 1976). In order to elucidate the various mechanisms of heavy-metal transport in the river, the clay of the bottom sediments and that carried in suspension was analysed for the metals at a number of locations and subjected to X-ray diffraction for the determination of the clay minerals present. The bottom sediments consist of kaolinite, illite, random interstratification (of mica and expandable layers) and quartz. In some samples chlorite and calcite were detected as well. The mineral content of the suspended load was collected by pressure filtration on porous ceramic plates. The clay minerals determined by subjecting the plates plus filtered residue to X-ray diffraction were the same as in the sediments. In addition to the clay-mineral reflections, three of the samples obtained from suspension (locations 2, 3, and 5 in the map, Fig. 1) showed the strongest diffraction line of the mineral brushite, CaHPO₄·2H₂O, at 7.6 Å. In one sample (location 2) three more lines of brushite were observed. The occurrence of brushite in the Neckar may be taken as a mineralogical indicator of the pollution of the river, because the following materials may be possible sources of the phosphate: artificial fertilizers, liquid manure, water softeners, detergents, and industrial waste waters.     

Theory of the collapsed zone at the front of a coal seam and its effect on translatory rock bursting

If the slope of the uniaxial stress–strain diagram in the post-failure regime is steep enough, it is shown, using a simplified (‘elementary’) theory, that the frontal zone of a coal seam close to a cavity may suddenly collapse. This collapse, well known from in situ, evidence, is also shown to reduce in most cases the danger of initiation or the strength of a subsequent coal mine bump.     

Experimental and theoretical bond critical point properties for model electron density distributions for earth materials

Generalized X-ray scattering factor model experimental electron density distributions and bond critical point, bcp, properties generated in recent studies for the earth materials stishovite, forsterite, fayalite and cuprite with high energy single crystal synchrotron X-ray diffraction data and those generated with high resolution diffraction data for coesite and senarmonite were found to be adequate and in relatively good agreement, ~5% on average, with those calculated with quantum chemical methods with relatively robust basis sets. High resolution low energy single crystal diffraction data, recorded for the molecular sieve AlPO₄-15, were also found to yield model electron density distribution values at the bcp points for the AlO and PO bonded interactions that are in relatively good to moderately good agreement with the theoretical values, but the Laplacian values of the distribution at the points for the two bonded interactions were found to be in relatively poor agreement. In several cases, experimental bcp properties, generated with conventional low energy X-ray diffraction data for several rock forming minerals, were found overall to be in poorer agreement with the theoretical properties. The overall agreement between theoretical bcp properties generated with computational quantum methods and experimental properties generated with synchrotron high energy radiation not only provides a basis for using computational strategies for studying and modeling structures and their electron density distributions, but it also provides a basis for improving our understanding of the crystal chemistry and bonded interactions for earth materials. Theoretical bond critical point properties generated with computational quantum methods are believed to rival the accuracy of those determined experimentally. As such the calculations provide a powerful and efficient method for evaluating electron density distributions and the bonded interactions for a wide range of earth materials.Dedicated to Professor Robert F. Stewart of Carnegie Mellon University on his retirement for his brilliant and original work modeling electron density distributions.     

Dating ultra-deep mine waters with noble gases and Cl, Witwatersrand Basin, South Africa

Concentrations and isotopic ratios of dissolved noble gases, ³⁶Cl, δD and δ¹⁸O in water samples from the ultra-deep gold mines (0.718 to 3.3 km below the surface) in the Witwatersrand Basin, South Africa, were investigated to quantify the dynamics of these ultra deep crustal fluids. The mining activity has a significant impact on the concentrations of dissolved gases, as the associated pressure release causes the degassing of the fissure water. The observed under saturation of the atmospheric noble gases in the fissure water samples (70-98%, normalized to ASW at 20°C and 1013 mbar) is reproduced by a model that considers diffusive degassing and solubility equilibration with a gas phase at sampling temperature. Corrections for degassing result in ⁴He concentrations as high as 1.55 · 10⁻¹cm³STP⁴He g⁻¹, ⁴⁰Ar/³⁶Ar ranging between 806 and 10331, and ¹³⁴Xe/¹³²Xe and ¹³⁶Xe/¹³²Xe ratios above 0.46 and 0.44, respectively. Corrected ^134(136)Xe/¹³²Xe and ^134(136)Xe/⁴He-ratios are consistent with their production ratios, whereas the nucleogenic ⁴He/⁴⁰Ar, and ^134(136)Xe/⁴⁰Ar ratios generally indicate that these gases are produced in an environment with an average [U + Th]/K-content 2-3 times above that of crustal average. In two scenarios, one considering only accumulation of in situ produced noble gases, the other additionally crustal flux components, the model ages for 14 individual water samples range from 13 to 168 Ma and from 1 to 23 Ma, respectively.The low ³⁶Cl-ratios of (4-37) · 10⁻¹⁵ and comparatively high ³⁶Cl-concentrations of (8-350) · 10⁻¹⁵ atoms ³⁶Cl l⁻¹ reflect subsurface production in secular equilibrium indicating an age in excess of 1.5 Ma or 5 times the half-life of ³⁶Cl.In combination, the results suggest residence times of the fluids in fissures in this region (up to 3.3 km depth) are of the order of 1-100 Ma. We cannot exclude the possibility of mixing and that small quantities of younger water have been mixed with the very old bulk.     

Solute transport in formations of very low permeability: profiles of stable isotope and dissolved noble gas contents of pore water in the Opalinus Clay, Mont Terri, Switzerland

Pore water profiles of water, stable isotope, and dissolved noble gas content have been determined across the Opalinus Clay and adjacent formations at the rock laboratory at Mont Terri. We have found enhanced helium contents (up to [⁴He] = 1 × 10⁻⁴ cubic centimeters at standard pressure and temperature per gram of pore water) and argon isotope ratios (⁴⁰Ar/³⁶Ar ratios up to 334) due to accumulation of ⁴He and ⁴⁰Ar produced in situ. The helium profile was found to be in steady state with respect to in situ production and diffusive loss into the adjacent limestones where groundwater circulates. From this profile a representative mean value of the apparent diffusion coefficient for helium in the pore water of the whole formation was derived for the first time to be D_a = 3.5 × 10⁻¹¹ m² · s⁻¹, which is more than two orders of magnitude lower than the diffusion coefficient D₀ in free water. The stable isotope profile, however, indicates a component of fossil marine pore water, which has not yet been replaced by molecular diffusion of meteoric water from the adjacent limestone and shale formations over the past 10 million years.     

Electron density distribution and bond critical point properties for forsterite, Mg2 SiO4, determined with synchrotron single crystal X-ray diffraction data

A generalized X-ray scattering factor model experimental electron density distribution has been generated for the orthosilicate forsterite, using an essentially extinction and absorption free set of single crystal diffraction data recorded with intense, high energy synchrotron X-ray radiation (E=100.6 keV). A refinement of the model converged with an R(F)=0.0061. An evaluation of the bond critical point, bcp, properties of the distribution at the (3, –1) stationary points for the SiO and MgO bonded interactions, yielded values that agree typically within ~5%, on average, with theoretical values generated with quantum chemical computational strategies, using relatively robust basis sets. On the basis of this result, the modeling of the experimental distribution is considered to be adequate. As the bcp properties increase in magnitude, the MgO and SiO bonds decrease in length as calculated for a number of rock forming silicates. As asserted by Coppens (X-ray charge densities and chemical bonding. Oxford University Press, Oxford, 1997), large negative ²(r_c) values, characteristic of shared interactions involving first row atoms, may not be characteristic of closed shell covalent bonded interactions involving second row Si, P and S atoms bonded to O. This study adds new evidence to the overall relatively good agreement between theoretical bcp properties generated with computational quantum strategies, on the one hand, and experimental properties generated with single crystal high energy synchrotron diffraction data on the other. The similarity of results not only provides a basis for using computational strategies for studying and modeling structures, defects and the reactivity of representative structures, but it also provides a basis for improving our understanding of the crystal chemistry of earth materials and the character of the SiO bonded interaction.     

Practical use of video imagery in nearshore oceanographic fieldstudies

An approach was developed for using video imagery to quantify, in terms of both spatial and temporal dimensions, a number of naturally occurring (nearshore) physical processes. The complete method is presented, including the derivation of the geometrical relationships relating image and ground coordinates, principles to be considered when working with video imagery and the two-step strategy for calibration of the camera model. The techniques are founded on the principles of photogrammetry, account for difficulties inherent in the use of video signals, and have been adapted to allow for flexibility of use in field studies. Examples from field experiments indicate that this approach is both accurate and applicable under the conditions typically experienced when sampling in coastal regions. Several applications of the camera model are discussed, including the measurement of nearshore fluid processes, sand bar length scales, foreshore topography, and drifter motions. Although we have applied this method to the measurement of nearshore processes and morphologic features, these same techniques are transferable to studies in other geophysical settings