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.     

Integral field spectroscopy with the GEMINI multiobject spectrographs

We describe the integral field unit (IFU) which converts the Gemini Multiobject Spectrograph (GMOS) installed on the Gemini-North telescope to an integral field spectrograph,which produces spectra over a contiguous field of view of 7 × 5 arcsec with spatial sampling of 0.2 arcsecover the wavelength range 0.4-1.0 μm.GMOS is converted to this mode by the remote insertion of the IFU into thebeam in place of the masks used for the multiobject mode. A separate fieldof half the area of the main field, but otherwise identical, is alsoprovided to improve background subtraction. The IFU contains 1500lenslet-coupled fibres and was the first facility of any type for integralfield spectroscopy employed on an 8/10 m telescope.We describe the design, construction and testing of the GMOS IFU and present measurements of the throughput both in the laboratory and at the telescope. We compare these with a theoretical prediction made before construction started. All are in good agreement with each other, with the on-telescope throughput exceeding 60% (averaged over wavelength). Finallywe show an example of data obtained during commissioning to illustrate the power of the device.     

Oxygen isotopic compositions and origins of calcium‐aluminum‐rich inclusions and chondrules

Abstract— Primary minerals in calcium‐aluminum‐rich inclusions (CAIs), Al‐rich and ferromagnesian chondrules in each chondrite group have δ¹⁸O values that typically range from ?50 to +5%0. Neglecting effects due to minor mass fractionations, the oxygen isotopic data for each chondrite group and for micrometeorites define lines on the three‐isotope plot with slopes of 1.01 ± 0.06 and intercepts of ?2 ± 1. This suggests that the same kind of nebular process produced the ¹⁶O variations among chondrules and CAIs in all groups. Chemical and isotopic properties of some CAIs and chondrules strongly suggest that they formed from solar nebula condensates. This is incompatible with the existing two‐component model for oxygen isotopes in which chondrules and CAIs were derived from heated and melted ¹⁶O‐rich presolar dust that exchanged oxygen with ¹⁶O‐poor nebular gas. Some FUN CAIs (inclusions with isotope anomalies due to fractionation and unknown nuclear effects) have chemical and isotopic compositions indicating they are evaporative residues of presolar material, which is incompatible with ¹⁶O fractionation during mass‐independent gas phase reactions in the solar nebula. There is only one plausible reason why solar nebula condensates and evaporative residues of presolar materials are both enriched in ¹⁶O. Condensation must have occurred in a nebular region where the oxygen was largely derived from evaporated ¹⁶O‐rich dust. A simple model suggests that dust was enriched (or gas was depleted) relative to cosmic proportions by factors of ～10 to >50 prior to condensation for most CAIs and factors of 1–5 for chondrule precursor material. We infer that dust‐gas fractionation prior to evaporation and condensation was more important in establishing the oxygen isotopic composition of CAIs and chondrules than any subsequent exchange with nebular gases. Dust‐gas fractionation may have occurred near the inner edge of the disk where nebular gases accreted into the protosun and Shu and colleagues suggest that CAIs formed.     

Large‐ion lithophile element fractionation during the early differentiation of Mars and the composition of the martian primitive mantle

Abstract— Basaltic shergottites display a systematic decrease in K/Th, K/U, and K/La ratios with increasing K content. These trends are interpreted as mixing lines between relatively young martian magmas derived from highly depleted mantle sources and an ancient large‐ion lithophile (LIL) element‐enriched crustal component. One implication of this is that a substantial fractionation of these ratios occurs during the early crustal differentiation on Mars. Isotopic evidence from SNC meteorites and compositional data from Pathfinder and orbital gamma ray spectroscopy suggest that in excess of 50% of the LIL element complement of Mars resides in the crustal reservoir. If so, the primitive mantle of Mars is significantly more volatile‐depleted (i.e., lower K/Th, K/U, K/La) than previously thought but probably (though not necessarily) still less volatile‐depleted than the primitive mantle of the Earth. The La/Th ratios of virtually all SNC meteorites are subchondritic, including those with the most severe LREE‐depletion. Extrapolation of the basaltic shergottite trend suggests that both the depleted mantle end member and the enriched crustal end member have subchondritic La/Th ratios. This is in contrast with the Earth where basalts from LIL element‐depleted sources such as MORB have superchondritic La/Th ratios, complementary to the subchondritic ratios of the continental crust. Accordingly, assuming that the refractory elements are in chondritic proportions for the Mars primitive mantle, an additional major geochemical reservoir must exist on Mars that may not yet have been sampled.