Effect of element size on the static finite element analysis of steep slopes

The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher‐order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd.     

The Effect of Atmospheric Drag on Satellite Orbits During the Bastille Day Event

Geomagnetic storms driven by solar eruptions are known to have significant effects on the total density of the upper atmosphere in the altitude range 250–1000 km. This in turn causes a measurable effect on the orbits of resident space objects in this altitude range. We analyzed a sample of these orbits, both from sensor data and from orbital element sets, during the period surrounding the 14 July 2000 solar activity. We present information concerning the effects of this event on the orbits of resident space objects and how well accepted atmospheric models were able to represent it. As part of this analysis, we describe a technique for extracting atmospheric density information from orbital element sets. On daily time scales, the effect of geomagnetic activity appears to be more important than that of prompt radiation. However, the limitations in time and amplitude quantization of the accepted solar indices are evident. A limited comparison is also made with previous solar storm events.     

A depleted, not ideally chondritic bulk Earth: The explosive-volcanic basalt loss hypothesis

It has long been customary to assume that in the bulk composition of the Earth, all refractory-lithophile elements (including major oxides Al₂O₃ and CaO, all of the REE, and the heat-producing elements Th and U) occur in chondritic, bulk solar system, proportion to one another. Recently, however, Nd-isotopic studies (most notably Boyet M. and Carlson R. W. (2006) A new geochemical model for the Earth’s mantle inferred from ¹⁴⁶Sm-¹⁴²Nd systematics. Earth Planet. Sci. Lett.250, 254-268) have suggested that at least the outer portion of the planet features a Nd/Sm ratio depleted to ∼0.93 times the chondritic ratio. The primary reaction to this type of evidence has been to invoke a “hidden” reservoir of enriched matter, sequestered into the deepest mantle as a consequence of primordial differentiation. I propose a hypothesis that potentially explains the evidence for Nd/Sm depletion in a very different way. Among the handful of major types of differentiated asteroidal meteorites, two (ureilites and aubrites) are ultramafic restites so consistently devoid of plagioclase that meteoriticists were once mystified as to how all the complementary plagioclase-rich matter (basalt) was lost. The explanation appears to be basalt loss by graphite-fueled explosive volcanism on roughly 100-km sized planetesimals; with the dispersiveness of the process dramatically enhanced, relative to terrestrial experience, because the pyroclastic gases expand into vacuous space (Wilson L. and Keil K. (1991) Consequences of explosive eruptions on small Solar System bodies: the case of the missing basalts on the aubrite parent body. Earth Planet. Sci. Lett.104, 505-512). By analogy with lunar pyroclastic products, the typical size of pyroclastic melt/glass droplets under these circumstances will be roughly 0.1 mm. Once separated from an asteroidal or planetesimal gravitational field, droplets of this size will generally spiral toward the Sun, rather than reaccrete, because drag forces such the Poynting-Robertson effect quickly modify their orbits (the semimajor axis, in a typical scenario, is reduced by several hundred km during the first trip around the Sun). Assuming a similar process occurred on many of the Earth’s precursor planetesimals while they were still roughly 100 km in diameter, the net effect would be a depleted composition for the final Earth. I have modeled the process of trace-element depletion in the planetesimal mantles, assuming the partial melting was nonmodal and either batch or dynamic in terms of the melt-removal style. Assuming the process is moderately efficient, typical final-Earth Nd/Sm ratios are 0.93-0.96 times chondritic. Depletion is enhanced by a relatively low assumed residual porosity in batch-melting scenarios, but dampened by a relatively high value for “continuous” residue porosity in dynamic melting scenarios. Pigeonite in the source matter has a dampening effect on depletion. There are important side effects to the Nd/Sm depletion. The heat-producing elements, Th, U and K, might be severely depleted. The Eu/Eu^∗ ratio of the planet is unlikely to remain precisely chondritic. One of the most inevitable side effects, depletion of the Al/Ca ratio, is consistent with an otherwise puzzling aspect of the composition of the upper mantle. A perfectly undepleted composition for the bulk Earth is dubious.     

The hydrochemistry of a semi-arid pan basin case study: Sua Pan,Makgadikgadi, Botswana

This study presents results on the fluid and salt chemistry for the Makgadikgadi, a substantial continental basin in the semi-arid Kalahari. The aims of the study are to improve understanding of the hydrology of such a system and to identify the sources of the solutes and the controls on their cycling within pans. Sampling took place against the backdrop of unusually severe flooding as well as significant anthropogenic extraction of subsurface brines. This paper examines in particular the relationship between the chemistry of soil leachates, fresh stream water, salty lake water, surface salts and subsurface brines at Sua Pan, Botswana with the aim of improving the understanding of the system’s hydrology. Occasionally during the short wet season (December–March) surface water enters the saline environment and precipitates mostly calcite and halite, as well as dolomite and traces of other salts associated with the desiccation of the lake. The hypersaline subsurface brine (up to TDS 190,000 mg/L) is homogenous with minor variations due to pumping by BotAsh mine (Botswana Ash (Pty) Ltd.), which extracts 2400 m³ of brine/h from a depth of 38 m. Notable is the decrease in TDS as the pumping rate increases which may be indicative of subsurface recharge by less saline water. Isotope chemistry for Sr (⁸⁷Sr/⁸⁶Sr average 0.722087) and S (δ³⁴S average 34.35) suggests subsurface brines have been subject to a lithological contribution of undetermined origin. Recharge of the subsurface brine from surface water including the Nata River appears to be negligible.     

The contribution of atmospheric acid deposition to ocean acidification in the subtropical North Atlantic Ocean

The absorption of anthropogenic CO₂ and atmospheric deposition of acidity can both contribute to the acidification of the global ocean. Rainfall pH measurements and chemical compositions monitored on the island of Bermuda since 1980, and a long-term seawater CO₂ time-series (1983–2005) in the subtropical North Atlantic Ocean near Bermuda were used to evaluate the influence of acidic deposition on the acidification of oligotrophic waters of the North Atlantic Ocean and coastal waters of the coral reef ecosystem of Bermuda. Since the early 1980's, the average annual wet deposition of acidity at Bermuda was 15 ± 14 mmol m^− 2 year^− 1, while surface seawater pH decreased by 0.0017 ± 0.0001 pH units each year. The gradual acidification of subtropical gyre waters was primarily due to uptake of anthropogenic CO₂. We estimate that direct atmospheric acid deposition contributed 2% to the acidification of surface waters in the subtropical North Atlantic Ocean, although this value likely represents an upper limit. Acidifying deposition had negligible influence on seawater CO₂ chemistry of the Bermuda coral reef, with no evident impact on hard coral calcification.     

The First Law of Thermodynamics in a salty ocean

The First Law of Thermodynamics is developed from fundamentals for open, non-equilibrium systems of seawater in motion, exchanging salt and freshwater internally and with their surroundings, and varying continuously in temperature, pressure, and salinity. The aim is clarity and consistency of concepts – and precision in the accompanying vocabulary. Particular attention is given to the way in which salinity variation plays out in the logical structures. The arbitrary constants in the thermodynamic potentials and the various First Law equations are highlighted, in order to remove them, and to recover the physically meaningful content. When this is done, it is seen that salinity variations have little consequence in application of the First Law to the ocean, apart from affecting values of coefficients.