Bending of fluid‐saturated linear poroelastic beams with compressible constituents

Analytical solutions are presented for fluid‐saturated linear poroelastic beams under pure bending. The stress‐free boundary condition at the lateral surfaces is satisfied in the St Venant's sense and the Beltrami–Michell compatibility conditions are resolved rigorously, rendering the flexure of the beams analytically tractable. Two sets of formulations are derived based on the coupled and uncoupled diffusion equations respectively. The analytical solutions are compared with three‐dimensional finite element simulations. Both sets of analytical formulations are capable of capturing exactly both the initial (undrained) and the steady‐state (fully drained) deflection of the beams. However, the analytical solutions are found to be deficient during the transient phase. The cause for the deficiency of the transient analytical solutions is discussed. The accuracy of the analytical solutions improves as Poisson's ratio and the compressibility of the constituents of the porous beam increase, where the St Venant's edge effect at the lateral surfaces is mitigated. Copyright © 2008 John Wiley & Sons, Ltd.     

Three Secondary Reference Materials for Lithium Isotope Measurements: Li7-N, Li6-N and LiCl-N Solutions

The CRPG (Nancy, France) has prepared secondary reference materials for Li isotope measurements by mixing ⁷Li or ⁶Li spikes and either L-SVEC or IRMM-016 certified reference materials to produce solutions having a known Li concentration and isotopic composition. The Li7-N and Li6-N solution samples (1.5 mol l⁻¹ HNO₃) have nominal δ⁷Li isotopic compositions of 30.1‰ and -9.7‰ respectively relative to L-SVEC and concentrations of 100 mg l⁻¹. Repeated measurement of these samples using the QUAD-ICP-MS at the CRPG yielded δ⁷Li of 30.4 ± 1.1‰ (n = 13) and -8.9 ± 0.9‰ (n = 9) at the 2s level of confidence. An additional LiCl-N solution was measured and yielded a delta value of 9.5 ± 0.6‰ (n = 3). Identical results were obtained at the BRGM (Orléans, France) from determinations performed with a Neptune MC-ICP-MS (30.2 ± 0.3‰, n = 89 for the Li7-N, -8.0 ± 0.3‰, n = 38 for the Li6-N and 10.1 ± 0.2‰, n = 46 for LiCl-N at the 2s level of confidence). The deviation of measured composition relative to the nominal value for the Li6-N solution might be explained by either contamination during preparation or an error during sample weighing. These secondary reference materials, previously passed through ion exchange resin or directly analysed, may be used for checking the accuracy of Li isotopic measurements over a range of almost 40‰ and will be available to the scientific community upon request to J. Carignan or N. Vigier, CRPG.     

ISO Best Practices in Reference Material Certification and Use in Geoanalysis

The International Organisation for Standardisation (ISO) has published many guides, or technical standards, of great value to analytical geochemists. Two of particular importance are Guide 33 (Uses of Certified Reference Materials) and Guide 35 (Certification of Reference Materials). Both were first developed in the 1980s and undergo regular review and updating by the Reference Materials Committee (REMCO) that operates within ISO. Recent revisions have focused on adding statistical rigour to both guides. Although this offers significant advantages for use by professional metrologists, there are consequent issues of comprehension by the analytical chemists who in fact have the greatest need of them. A major focus of Guide 35 is the development of reference material uncertainties that are in full compliance with the Guide on Measurement Uncertainty (GUM), jointly issued by ISO, IUPAC and others. Guide 35 details handling of uncertainty due to (1) degradation on the shelf and in transport, (2) sample heterogeneity and (3) inter‐method and inter‐laboratory bias, as well as within‐laboratory repeatability. The International Association of Geoanalysts has developed a protocol for reference material certification that applies Guide 35 to the specific needs of the geoanalytical community. The approach being taken by the IAG in developing GUM‐compliant uncertainties for its certified values is presented. Recommendations made in Guide 33 for how a laboratory should compare its own results with certified values in assessing laboratory accuracy are outlined. Additionally, the subject of misusing reference materials is discussed. The apparent misuse occurs because so few CRMs exist that meet critical measurement needs of geoanalytical laboratories and that also meet the rigorous metrological demands of the latest editions of the ISO Guides. All of the focus of the IAG certification programme has been to undertake certifications that would fill gaps in CRM availability and thus serve to limit this misuse.     

On the individual calibration of hailpads

This paper is a comparative study between the two most common hailpad calibration systems: one annual calibration of a whole consignment of material, and the individual calibration of each plate after a hailfall. Individual calibration attempts to minimize errors due to differences in sensitivity to the impact of hailstones between plates from the same consignment, or due to differences in the inking process before the actual measurement.The comparison was carried out using calibration data from the past few years in the hailpad network in south-western France, and data from an individual calibration process on material provided by the hailpad network in Lleida (Spain). The same type of material was used in the two cases.The results confirm that the error in measuring hailstone sizes is smaller in the case of an individual calibration of hailpads than when one single calibration process was carried out for a whole consignment. The former is approximately 80% of the latter. However, this error could have been higher if it had not been the same person carrying out the single calibration process and the measuring of the dents: it has been found that differences in the inking process may account for up to 20% of the error in the case of small hailstones. Calibration errors affecting other variables, e.g. energy or parameter λ of the exponential size distribution are generally higher (5% and 18%, respectively) than errors due to the spatial variability of the hailstones. However, the calibration method does not influence the maximum size, since the relative error attributed to the spatial variability is about 8 times the calibration error.In conclusion, if errors in determining energy or parameter λ are to be reduced to a minimum, it is highly advisable to be consistent in applying the measuring procedure (if possible with the same person carrying out the measurements all the time), and even to use individual calibration on each plate, always bearing in mind that technicians have to be trained appropriately in order to achieve the highest possible degree of uniformity.     

Ostracods and palaeobotany from the middle Permian of Oman: implications on Pangaea reconstruction

Discovery of a middle Permian ostracod fauna in the marine Khuff Formation (Sultanate of Oman), combined with palaeobotanical data from the immediately underlying continental Gharif Formation, supports new interpretations of the palaeobiogeography of the Tethys during the late Palaeozoic. A mixed ostracod fauna existed on the Arabian platform. This new record of Permian ostracods, combined with recent data obtained in other Tethyan areas, emphasizes the close relationship between the south-western Tethys realm and South China. The macro- and microfloral assemblages of the continental Gharif Formation demonstrate that this palaeoflora represents a true mixed association in which Gondwanan, Cathaysian and Euramerian elements are intermingled. Two main models exist for the reconstruction of Pangaea during the late Palaeozoic. Both ostracods and palaeobotanical evidence favour the reduction of the oceanic area between South China and Arabian plate as in the B Pangaea model favoured by recent palaeomagnetic data.     

Les concentrations à sillimanite du Sud Velay et l'évolution P–T–t fini-hercynienne dans le Massif central (France)

The Late Hercynian evolution in the French Massif Central corresponds to the transition from a LP–HT (M₃ event at 314 ± 5 Ma) to a higher temperature metamorphism corresponding to the emplacement of the Velay granite dome (M₄ event at 301 ± 5 Ma). This transition is outlined by the development of sillimanite folia, which represent planes of base-cation leaching, associated with ductile deformation. This evolution implies a counterclockwise retrograde $P\text{–}T\text{–}t$ path under subsolidus conditions between M₃ and M₄. To cite this article: P. Barbey et al., C. R. Geoscience 337 (2005).     

Trace element partitioning in plagioclase feldspar

Compilation and interpretation of experimental and natural Nernst partition coefficient (^{plagioclase/melt}D) data show that, with a few exceptions, increases in ^{plagioclase/melt}D correlate with decreasing anorthite-content of plagioclase. In contrast, increases of ^{plagioclase/melt}D for Ga, Sc, Cu, Zn, Zr, Hf and Ti, are better correlated against decreasing melt MgO or increasing melt SiO₂ contents. ^{plagioclase/melt}D for Ti and the rare earth elements (REE) show little dependence on temperature, but increase as the melt water content increases. ^{plagioclase/melt}D for K and Sr are sensitive to pressure. Variations of D₀ (the strain compensated partition coefficient), r₀ (the size of the site into which REE substitute), and E (Young’s Modulus of this site) were parameterized against variations of melt SiO₂, the An-content of plagioclase, and other combinations of variables, allowing ^{plagioclase/melt}D_REE-Y to be calculated from a variety of input parameters. The interrelations of temperature, melt MgO and SiO₂ content, and plagioclase anorthite-content for wet and dry systems were also parameterized to facilitate interpolation where such data are lacking. When combined, these semi-empirical parameterizations yield ^{plagioclase/melt}D results comparable to available experimental and natural data.     

Détermination des masses des planétes

Sans résumé

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Presented at IAU Colloquium No. 9, The IAU System of Astronomical Constants', Heidelberg, Germany, August 12–14, 1970.