A variational inequality approach to free surface seepage in an inhomogeneous dam

The current work uses Baiocchi's transformation to obtain heuristically a formulation of the inhomogeneous dam problem. When finite element methods are applied the finite dimensional problem is a variational inequality which may be solved to obtain approximate solutions. The main advantage of the method is that it uses a fixed mesh. The finite dimensional problem is solved by means of succesive overrelaxation with projection. Although the standard convergence theory¹ for this method does not apply in this case, because the stiffness matrix is not symmetric, satisfactory and rapid convergence was obtained in all of our examples. Numerical results are given for some examples.     

Structure-composition relations and Raman spectroscopy of high-pressure sodium silicates

?-Na₂Si₂O₅, ζ-Na₂Si₂O₅, Na₂Si[Si₂O₇], and Na₆Si₃[Si₉O₂₇] have been synthesized using an MA6/8 superpress. Densification in high-pressure sodium silicates is effected largely by changes in packing. In the relaxed (1 bar) structures, cation polyhedra and thermal/displacement parameters are similar to those of low-pressure silicates, but the extra-framework cation positions are oversized. The two mixed ^[4]Si and ^[6]Si framework silicates of known structure (Na₂Si[Si₂O₇] and Na₆Si₃[Si₉O₂₇]) belong to the limited homologous series Na_2mSi_m[Si_n–mO_2n+m], with m<n. The structure-composition relationships of wadeite-type, A₂Ge₄O₉-type, and Na₆Si₃[Si₉O₂₇] silicates and germanates depend on T-O distance and size of the large extra-framework cation. Characteristic features of the SiO₄ tetrahedral units are present in micro-Raman spectra of mixed ^[4]Si and ^[6]Si framework silicates, but bands uniquely attributable to SiO₆ octahedra are weak or obscured. However, ^[6]Si has a profound indirect influence on the Raman spectra, resulting in intense and complex low-frequency bands, assigned to symmetric bending modes with coupled displacements at both bridging oxygens and nonbridging oxygens bonded to ^[6]Si, and a shift to higher frequency and reduction in intensity of the high-frequency bands assigned to symmetric ^[4]Si-O_nbr stretching vibrations. Raman spectroscopy does not appear to be a useful structural probe for small amounts of ^[6]Si in silicate glasses and melts.     

The geochemistry of vanadiferous magnetite in the bushveld complex: Implications for crystallization mechanisms in layered complexes

Detailed trace-element analyses of pure magnetite from four continuous borehole intersections through the main magnetitite layer from the upper zone of the Rustenburg Layered Suite of the Bushveld Complex are presented. One section has been analysed at one centimetre intervals. Rapid depletion of Cr occurs over short, vertical sequences near the base of the layer, which is due to bottom-crystallization and the resulting chemical depletion of a thin layer of liquid. Sudden increases in Cr content of magnetite are attributed to convection cells which bring undepleted magma into the zone or crystallization. We suggest that these cells individually have lateral extents no greater than hundreds of metres, but collectively may be traced at a specific stratigraphic horizon for several tens of km. This lateral traceability of the effect of convection cells at approximately uniform stratigraphic height demonstrates the long-held implicit assumption that time-planes are in general parallel to the layering, and does not support the hypothesis that layers in the Bushveld Complex grew laterally. The activity of these cells is highly variable, with long periods of quiescence interspersed with periods of rapid, small-scale overturn. Most convection cells do not impinge upon the floor, and the abruptness of the resulting chemical reversal is largely a function of the thickness of the layer of depleted liquid trapped between the cumulates and the sole of the convection cell. Occasionally, these cells do touch the cumulate pile and may even cause erosion. This material may be redeposited elsewhere in the magnetitite layer either as mineralogically distinct fragments if erosion penetrated below the layer or, in the present instance, as a chemically chaotic pile of magnetite. The abruptness of the chemical reversals severely restricts the extent to which post-cumulus redistribution of elements or re-equilibration with percolating trapped liquid (infiltration metasomatism) may have occurred. The appearance of disseminated plagioclase in magnetite layers in variable proportions and in a non-systematic manner in the four profiles is attributed to fluctuations in pressure.     

Potassium-argon ages and strontium isotope ratio measurements from volcanic rocks in northeastern Nigeria

The Cenozoic volcanic activity in northeastern Nigeria began with the intrusion into the Benue trough of a trachyte-phonolite suite of plugs 22-11 m.y. ago. Later activity, which was more widespread and dominantly basaltic in character, began some 7 m.y. ago and has continued until very recent times. It resulted in basaltic plugs and lava plateaux within the Benue trough, and cinder cones and lavas on the Jos Plateau.The initial ⁸⁷Sr/⁸⁶Sr ratios of nine of the fifteen analyzed basic and alkalic rocks lie in the range 0.7025–0.7032, and the highest ratio measured is 0.7129.The main group of trachytes and phonolites are considered to be fractional melts derived from the upper mantle, modified in small part by potassium feldspar crystal fractionation. Two Sr-rich phonolite plugs may have a separate origin from the main group of trachytes and phonolites.The Cenozoic volcanic activity in northeastern Nigeria is probably related to the nearby Cameroun volcanic line. The concentration of plugs within the Benue trough may reflect internal adjustments along old lines of weakness within the African lithosphere plate, in response to synchronous changes affecting the plate's external dimensions and internal structure, such as the growth of the Red Sea and the Gulf of Aden, and the volcanism of the east African rift valley.     

On the lack of a unique relation between CO2 partial pressure and temperature in geothermal system. Comment on “Geothermal mineral equilibria” by W. F. Giggenbach

Giggenbach (1981) has proposed a relation of van't Hoff form, log₁₀P_CO2 = A ? B/(t + 273), between temperature and CO₂ partial pressure in deep liquid in geothermal systems. The proposed values for the coefficients are A = 15.26, B = 7850.The proposal is not supported by pressure-temperature data used by Giggenbach, and a survey of different fields indicates that the proposal is not valid.     

On the use of the nephelometer in estuarine waters

A study of the problems encountered in nephelometric determinations of suspended sediment loads in the Chesapeake Bay estuary has led to development of a technique which uses nephelometer readings as a guide for sampling at vertical profiles in an estuary. This permits optimum sampling for concentration profiles and allows one to use nephelometer/load ratios to characterize particles.     

A strontium isotope and trace element profile through the Partridge River Troctolite,Duluth complex,Minnesota

Initial ⁸⁷Sr/⁸⁶Sr ratios down a 2,315 foot-long core (DDH-295) through the Partridge River Troctolite are lower in the depth range 710–1,410 feet (0.70443±22) than in the underlying and overlying rocks (0.70500±18). These initial ratio variations define three zones (I, II, and III) thought to be three intrusive units within the troctolite. The best estimate of the Rb-Sr age of the troctolite is 1,050±105 m.y. The olivine compositions and the abundances of the incompatible trace elements Zr, Y, and Rb show identical variations down the core, with downward repetitions of olivine iron-enrichment and incompatible trace element enrichments. Discontinuities in the olivine compositions and incompatible trace element abundances match the initial ⁸⁷Sr/⁸⁶Sr ratio discontinuities in the core. The strontium isotope data imply that involatile components of the Proterozoic Virginia Formation and other Archaean rocks were not significantly assimilated by the troctolites, for only three out of the twenty-three initial ⁸⁷Sr/⁸⁶Sr ratios depart from normal magmatic values. These three anomalous ratios are not systematically related to the Cu-Ni sulphide mineralization and may be the result of secondary calcite in the troctolite. The strontium isotope systematics of the Virginia Formation xenoliths and underlying hornfelses are highly disturbed as a result of Rb loss. The apparently inverted fractionation sequences in the troctolites are interpreted in terms of downward increases in intercumulus liquid in repeated magma batches and controlled by plagioclase flotation. The amount of intercumulus liquid is estimated to range from 7 to 61 weight per cent. The Cu-Ni sulphides are concentrated in the lower 250 feet of zone I (immediately above the Virginia Formation) and through 400 feet of core across the contact between zones I and II, more than 750 feet above the base. Because the sulphide-bearing troctolites are not systematically related to disturbances in the magmatic initial ⁸⁷Sr/⁸⁶Sr ratios, the mineralization probably involved the volatile transfer of sulphur derived from dehydration reactions in the underlying Virginia Formation.     

Immobilization of strontium during iron biomineralization coupled to dissimilatory hydrous ferric oxide reduction

The potential for incorporation of strontium (Sr) into biogenic Fe(II)-bearing minerals formed during microbial reduction of synthetic hydrous ferric oxide (HFO) was investigated in circumneutral bicarbonate-buffered medium containing SrCl₂ at concentrations of 10 μM, 100 μM, or 1.0 mM. CaCl₂ (10 mM) was added to some experiments to simulate a Ca-rich groundwater. In Ca-free systems, 89 to 100% of total Sr was captured in solid-phase compounds formed during reduction of 30 to 40 mmol Fe(III) L⁻¹ over a 1-month period. A smaller fraction of total Sr (25 to 34%) was incorporated into the solid phase in cultures amended with 10 mM CaCl₂. X-ray diffraction identified siderite and ferroan ankerite as major end products of HFO reduction in Ca-free and Ca-amended cultures, respectively. Scanning electron microscopy-energy dispersive x-ray spectroscopy revealed the presence of Sr associated with carbonate phases. Selective extraction of HFO reduction end products indicated that 46 to 100% of the solid-phase Sr was associated with carbonates. The sequestration of Sr into carbonate phases in the Ca-free systems occurred systematically according to a heterogeneous (Doerner-Hoskins) partition coefficient (D_D-H) of 1.81 ± 0.15. This D_D-H value was 2 to 10 times higher than values determined for incorporation of Sr (10 μM) into FeCO₃(s) precipitated abiotically at rates comparable to or greater than rates observed during HFO reduction, and fivefold higher than theoretical partition coefficients for equilibrium Fe(Sr)CO₃ solid solution formation. Surface complexation and entrapment of Sr by rapidly growing siderite crystals (and possibly other biogenic Fe(II) solids) provides an explanation for the intensive scavenging of Sr in the Ca-free systems. The results of abiotic siderite precipitation experiments in the presence and absence of excess Ca indicate that substitution of Ca for Sr at foreign element incorporation sites (mass action effect) on growing FeCO₃(s) surfaces can account for the inhibition of Sr incorporation into the siderite component of ankerite formed in the Ca-amended HFO reduction experiments. Likewise, substitution of Fe(II) for Sr may explain the absence of major Sr partitioning into the calcite component of ankerite. The findings indicate that under appropriate conditions, sequestration of metals in siderite produced during bacterial Fe(III) oxide reduction may provide a mechanism for retarding the migration of Sr and other divalent metal contaminants in anaerobic, carbonate-rich sedimentary environments.     

Induced stress and microseismicity in the 3000 Orebody, Mount Isa

Summary The 3000 Orebody is one of two orebodies in the Deep Copper Mine at Mount Isa, Australia. Owing to concerns about potential shaft pillar instabilities, an integrated seismic system was introduced to monitor seismic activity associated with pillar and country rock deformation. Coupled with numerical modelling of the stress regime, the system may assist in the characterization of rock mass damage resulting from mining, and perhaps the identification of near- and far-field geological structures that affect stope performance. A study was undertaken to quantify the seismicity and to determine potential applications of the seismic technology. The relation between geological structure and seismicity is strong, suggesting good prospects for the use of the system in the ground-control activities noted above. The induction of seismicity, which involves small magnitude events, is associated with reduction of normal stress on planes of weakness, suggesting that stress path may be an important factor in the level of seismicity observed in hard rock mines.