Pre‐ and post‐test mathematical modelling of a plan‐asymmetric reinforced concrete frame building

Pre‐ and post‐test analyses of the structural response of a three‐storey asymmetric reinforced concrete frame building were performed, aimed at supporting test preparation and performance as well as studying mathematical modelling. The building was designed for gravity loads only. Full‐scale pseudo‐dynamic tests were performed in the ELSA laboratory in Ispra. In the paper the results of initial parametric studies, of the blind pre‐test predictions, and of the post‐test analysis are summarized. In all studies a simple mathematical model, with one‐component member models with concentrated plasticity was employed. The pre‐test analyses were performed using the CANNY program. After the test results became available, the mathematical model was improved using an approach based on a displacement‐controlled analysis. Basically, the same mathematical model was used as in pre‐test analyses, except that the values of some of the parameters were changed. The OpenSees program was employed. Fair agreement between the test and numerical results was obtained. The results prove that relatively simple mathematical models are able to adequately simulate the detailed seismic response of reinforced concrete frame structures to a known ground motion, provided that the input parameters are properly determined. Copyright © 2006 John Wiley & Sons, Ltd.     

Gravitational effect of distant Earth relief within the territory of former Czechoslovakia

We analyzed the gravitational effect of topography and bathymetry beyond the angular distance of approximately 1.5 degrees (referred to as the distant relief effect or DRE), and its impact on measured gravity values in the region of the former Czechoslovakia. Our work was strongly motivated by the contents of the pioneering contribution of outstanding Czech geophysicists Miloš Pick, Jan Pícha and Vincenc Vyskočil, which appeared at the turn of the 1950’s and 1960’s. Our numerical calculations were based upon the direct evaluation of the gravitational effects of compartments of a spherical layer, while the respective heights and depths were obtained from the 2 × 2 minutes digital elevation model (DEM) ETOPO2, taking into consideration also the influence of distant bathymetry. Our results are in close agreement with, but not identical to, those of the above cited authors. We also analyzed the influence of the grid cell size of the involved DEM upon the calculation results. We introduced an approximation of the analyzed effect, based on a simple linear relationship between the calculation point height, the DRE and its vertical gradient (VGDRE). Since when calculated at zero elevation the involved quantities DRE and VGDRE are smooth functions of latitude and longitude and can be easily interpolated, the approximation gives acceptable results in terms of desired accuracy of several μGal (1 μGal = 10⁻⁸ m/s²). In general, we can state that within the territories of the Czech and Slovak Republics the studied distant relief effect has negligible impact upon local gravity survey data. However, when applied to regional gravity studies, there could be a question of its possible influence in the form of a quasilinear W-E trend ranging approximately from −106.6 to −102.5 mGal within the territory of former Czechoslovakia. If we wanted to correct for this phenomenon, we should subtract this negative quantity from the standard Bouguer anomalies as they have been defined in the recent geophysical literature, thereby considerably increasing their values. But, instead of straightforward correcting the Bouguer anomalies for DRE only, we would rather recommend to wait until after the crustal and even lithospheric effects have been studied more carefully based upon the present day independent knowledge about the deep seated sources of those effects.     

Magmatic and hydrothermal R.E.E. fractionation in the Xihuashan granites (SE China)

The Xihuashan stock (South Jiangxi, China) is composed of cogenetic granitic units (granites Xe, a, c, d and b) and emplaced during the Yanshanian orogeny (153±0.2 Ma). They are two feldspars, Fe-rich biotite±garnet and slightly peraluminous granites. Primary accessory minerals are apatite 1, monazite, zircon, uranothorite±xenotime in granites Xe and a, zircon, uranothorite, uraninite, betafite, xenotime 1; hydrothermal minerals are monazite altered into parisite and apatite 2, Y-rich parisite, yttroparisite, Y-rich fluorite and xenotime 2 in granites c and b. Petrographic observations, major element, REE, Y and Rb–Sr isotropic data point to a magmatic suite (granites Xe and a granites c and d granite b) distinct from hydrothermal Na-or K-alteration of b. From granite Xe to granite b, LREE, Eu, Th and Zr content are strongly depleted, while HREE, Y and U content increase. During K-alteration of b, these variations are of minor importance. Major and accessory mineral evidences, geochemical and fluid inclusion results indicate two successive alteration fluids interacting with b, (1) a late-magmatic F^– and CO₂–rich fluid and (2) a post-magmatic, aqueous and slightly saline fluid. The depletion of LREE and Th content and the increase in HREE, Y and U content correspond, in the magmatic suite to the early fractionation of monazite in the granites where there is no hydrothermal alteration (granites Xe and e) and to the hydrothermal alteration of monazite into parisite and secondary apatite, intense new formation of yttroparisite, Y enrichment and U loss in the uranothorite and late crystallization of uraninite in the granites c and b. Moreover, simulated crystallization of monazite and temperature of monazite saturation show early fractionation of monazite from the magma in the less evolved granites (Xe and e) and prevailing hydrothermal leaching of monazite in the most evolved granites (c-d and b) related to a late-magmetic event. The slight variations of REE, Y, Th and U content in the K-altered granites compared to granite b emphazes the distinct chemical nature of the successive hydrothermal fluids. Rb–Sr and Sm–Nd isotopic results point to a 30 Ma period of time between the late-magmatic and the post-magmatic fluid circulation.     

On the inelastic seismic response of asymmetric buildings under bi‐axial excitation

The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

Lemniscate representation for inversion of gravity and magnetic data through nonlocal optimization

A method of representing surfaces and volumes by a set of geometric points and a small set of auxiliary parameters, based on generalization of Bernoulli’s notion of lemniscates is introduced. It provides for easy generation and modification of surfaces and volumes, which could be connected, disjoint or even with very irregular boundaries. This allows solving geophysical inversion problems, without constraining the anomalous volumes to some ideal or simple forms. This is illustrated by the example of joint inversion of gravity and magnetic data sets attributable to two-dimensional anomalous bodies. A nonlocal optimization algorithm calledsegmented Hamming scan is used for inversion. Comparison with nonlinear least-squares algorithm shows the advantages of the chosen approach. The concepts ofdesideratal andprocedural detours are illustrated.     

Bernstein preprocessing for nonlinear least squares inversion of gravity and magnetic data

Nonlinear, nonlocal and adaptive optimization algorithms, now readily available, as applied to parameter estimation problems, require that the data to be inverted should not be very noisy. If they are so, the algorithm tends to fit them, rather than smoothening the noise component out. Here, use of Bernstein polynomials is proposed to prefilter noise out, before inversion with the help of a sophisticated optimization algorithm. Their properties are described. Inversion of gravity and magnetic data for basement depth estimation, singly and jointly, and without and after Bernstein-preprocessing is conducted to illustrate that the inversion of Bernstein-preprocessed gravity data alone may be slightly superior to the joint inversion of gravity and magnetic data.     

The influence of a local heat source on a borehole temperature curve

Summary The paper describes a simple mathematical method of estimating the location and water yield of an underground water source by measuring the temperature in a borehole.