Insight on 2D- versus 3D-modelling of surface foundations via strength-of-materials solutions for soil dynamics

To simplify the analysis, three-dimensional soil–structure interaction problems are often modelled by considering a two-dimensional slice without changing the material properties of the soil. This procedure, although convenient, is of questionable validity because two-dimensional modelling inherently overestimates the radiation damping for translational and rocking motions. To make matters worse, two-dimensional modelling always entails an underestimation of the dynamic-spring coefficient for the translational motions. The damping ratio of the two-dimensional case, which is proportional to the ratio of the damping coefficient to the spring coefficient, will thus be even larger. Thus, reliance upon a two-dimensional analysis based on an equivalent slice of a strip foundation may result in a dangerously non-conservative design. Valuable insights into the essence of radiation damping and the difference between two-dimensional and three-dimensional models may be obtained via approximate strength-of-materials solutions based on cone–wedge models and travel-time considerations. By examining the decay of the waves along the axes of the cone–wedge models, the essence of radiation damping can be grasped. The heuristic concept of more spreading of waves in three dimensions than in two is misleading. Indeed, just the opposite is true: The less the amplitude spreads and diminishes with distance, the greater is the radiation damping. Because the damping ratio is grossly overestimated, two-dimensional modelling of a three-dimensional case cannot be recommended for actual engineering applications. It is more feasible to take the opposite approach and idealize slender soil–structure interaction problems with a radially symmetric model. As an alternative, when defining the equivalent slice of the two-dimensional strip foundation, the impedance of the soil can be changed to achieve a much better agreement of the high-frequency limits of the damping coefficients. In the low-frequency range this modified two-dimensional model also overestimates radiation damping, although to a lesser extent. As a by-product, the dimensions of the equivalent slice of a two-dimensional strip foundation are discussed; and equations for the aspect ratios determining the opening angles of the corresponding wedges are derived. Also addressed is the quite separate but related topic of the transition from square to slender rectangular foundations.     

Rotational cone models for a soil layer on flexible rock half-space

The unfolded cone model used for calculating the dynamic response of a disk on the surface of a soil layer resting on flexible rock for translational motion is extended to rotational motion. The method is analogous to that for a layer on rigid rock, the only modification being that the reflection coefficient – α replaces the coefficient of total reflection – 1. The modified value of – α, which, in general, is frequency-dependent, is determined by considering one-dimensional wave propagation along the cone for the first impingement at the layer–rock interface. The low- and high-frequency limits of – α for the rotational motion are the same as for translational motion. As these limits do not depend on frequency, the dynamic analysis using cones can be performed in the familiar time domain. The transfer function constructed by addressing the reflections–refractions at the soil–rock interface and the reflections at the free surface in the unfolded cone model is highly accurate, resulting in the same accuracy of the dynamic response of a disk on a layer resting on flexible rock as that on a homogeneous half-space modelled with a cone.     

Seismic response due to travelling shear wave including soil-structure interaction with base-mat uplift

The seismic response due to a travelling shear wave is investigated. The resulting input consists of a translational-and a torsional-acceleration time history, which depend on the ratio of the wavelength to the dimension of the footing. A nuclear reactor building is used for illustration. The combined result of the translational and torsional elastic response (the latter arises even in an axisymmetric structure) will not, in general, be larger than that encountered in the case of a spatially uniform earthquake. If the footing slips or becomes partially separated from the soil, a non-linear dynamic analysis has to be performed to determine the response. Substantial motions in all three directions will take place. The peak structural responses and the floor-response spectra are found to be highly non-linear for high acceleration input values.     

Response of a nuclear power plant on aseismic bearings to horizontally propagating waves

The nuclear island of Koeberg with a large basemat, a non-linear base isolation effective in the horizontal direction only, founded on rock, is analysed for inclined body waves and for a combination of surface and body waves associated with prescribed horizontal and vertical components of the control motion. When compared to vertical incidence, an additional rocking component arises, generated by the horizontally propagating vertical component. As the aseismic bearings do not isolate against this rocking component, the corresponding horizontal response bears comparison with that of a conventional structure. The ratio of the response for horizontally propagating waves and that for vertically incident waves is thus considerably larger for the base-isolated structure than for a conventional one. However, the actual design incorporating other loading cases is affected much less.     

Hebung — Spaltung —? Grabenbildung im saxonischen und im ostalpinen Bereich

Zusammenfassung Wir fassen zusammen: Die hier betrachteten Grabenbildungen aus Niederhessen-Hannover, aus Schlesien und aus den steirischen Alpen lassen keinerlei Gründe für eine Entstehung durch Spaltung infolge Wölbung erkennen. Eine durchgängige Bindung an Schilde ist nicht vorhanden. Im Gegenteil, soweit die Gräben größeres Ausmaß besitzen, haben sie sich aus flach eingemuldeten Senkungszonen entwickelt, die breiter als die späteren Grabenstreifen waren. Nur im Solling mag Spaltung durch Wölbung für die Anlage der Gräben eine Rolle gespielt haben, eine darüber hinausgehende beträchtliche Zerrung hat aber auch hier stattgefunden. Der starke Anteil von horizontalen Bewegungskomponenten ausweitender und einengender Art nach wechselnden Richtungen in der saxonischen Tektonik des Oberstockwerkes dürfte auf die Salzunterlage zurückzuführen sein, infolge welcher die postsalinare Decke auch bei Impulsen oder bei einem Gefälle, das durch mehr vertikale Bewegungen des variscischen Untergrundes zustandekam, leicht Gleitbewegungen ausführte. Der stärker vertikale Charakter der streifenförmigen Einsenkungen in den Untergrund ist bei fehlendem Salz an der saxonischen Tektonik Schlesiens und der jungmiozänen Tektonik der Ostalpen erkennbar. Die Richtung der Gräben (wie auch der vorangegangenen epirogenen Einmuldungen) ist streng von der Textur des Untergrundes abhängig.     

Field criteria for epigenetic-supergene versus sedimentary-diagenetic silica concentrations in cretaceous limestones,Chihuahua, Mexico

The Cretaceous limestones of Chihuahua, Mexico, exhibit both sedimentary-diagenetic and epigenetic-supergene silica deposits which are distinguished from each other on the basis of texture/fabric/structure, composition, colour, presence or absence of certain other minerals such as malachite and/or hematite, structural relationships with the host-rock, and general paragenetic characteristics with each other; all described herein. The criteria offer a useful composite working model during field work.     

Preliminary studies of food habits of juvenile fish,China Poot Marsh and Potter Marsh,Alaska, 1978

During the year 1978, juvenile salmonids were collected from coastal streams running through China Poot Marsh and the stomach contents analyzed. Stomach contents of threespine stickleback (Gasterosteus aculeatus) and staghorn sculpin (Leptocottus armatus) from China Poot and of threespine stickleback from Potter Marsh were also analyzed; these two species were generally caught in tidal pools on the marshes. The juvenile coho salmon (Oncorhynchus kisutch) had the most varied diet; 37 different prey items were identified in the stomachs. By comparison, 25, 26, and 33 prey taxa were identified in the stomach contents of Dolly Varden char (Salvelinus malma), threespine stickleback, and staghorn sculpin, respectively. Amphipods were the dominant prey of all fish collected from China Poot Marsh; chironomidae larvae were the most common item in the stomach contents of threespine stickleback from Potter Marsh. The diets of all species changed over the course of the study period; the change was most dramatic for juvenile salmonids and sculpins.     

Bindungsverhalten ausgewählter Elemente in Sedimenten eines sauren Tagebaurestsees/FNR>

Binding Character of Selected Elements in Acidic Mining Lake Sediments To investigate the vertical element distribution in an acidic mining lake the concentrations of selected elements were measured by ICP‐MS and ICP‐OES. By knowing the metal concentrations in different depths it is possible to divide these metals into three groups. While the concentrations of iron, manganese, and zinc decline with decreasing depth, those of aluminium, copper, and nickel rise up. For lead and cobalt no distinct tendency could be determined. The limit value for all measured elements was not exceeded in any sampling location. The binding character of the metals is, besides the seasonal conditions of the lake (circulation in spring and stagnation in summer), influenced by the sediment depth. The addition of Carbokalk® for lake water neutralization had no significant effect on binding character of the analyzed metals. The application of a sequential extraction procedure enabled a classification of the available metal binding forms. All analyzed metals occurred mainly in compounds which are difficult to mobilize and for environment only slightly available.     

Chemistry, small-scale inhomogeneity, and formation of moldavites as condensates from sands vaporized by the Ries impact

The formation of the Ries impact and the moldavites have identical radiogenic ages of 14.3 Ma. According to this conformity in age moldavites are generally regarded as products of the Ries impact. This paper, which is divided into two sections, deals with two aspects of the moldavite-forming process: the formation of moldavite bodies by accretion of small precursors, and the physical and chemical conditions under which these primary units originated from sands which covered the Ries impact site.First, the chemical inhomogeneity of moldavite glasses is investigated in sections of 11 moldavites, using back scattered electron (BSE) images and electron microprobe analyses on 0.4-2.7 mm long traverses. Schlieren and lechatelierite particles are interpreted as relics of small, chemically different precursors, which accumulated to larger moldavite bodies at temperatures too low to be efficient for mixing. The patterns of schlieren and lechatelierite inclusions represent two successive rheological regimes: Small agglomerating primary melt units were extended into thin lamellae and threads under conditions of laminar flow. As evidenced by folded textures, these fluidal arrays were later plastically deformed under conditions of compressional stress.To elucidate the production of the primary melt units by the Ries impact, in the second section the geologic situation of the Ries area is considered with regard to possible source materials. The site of the Ries impact, situated at the northern border of the pre-Alpine Molasse basin, was covered at the time of the impact by fluviatile sediments of the lower sequence of the Obere Süßwasser-Molasse (OSM) Formation of Middle Miocene age, consisting of sands, marly sands and clays. Chemical analyses for major and trace elements of 38 moldavites from Bohemia and Moravia, and of 28 samples of the OSM Formation, collected from outcrops and drill holes, immediately south of the Ries crater and south of the Danube, show chemical conformity of moldavites and sand samples with regard to the major parameters SiO_2,Al₂O₃+ FeO, and MgO + CaO, indicating that these sands were the essential source material of moldavites. But, differences in contents of individual major and trace elements between moldavites and sands show that the formation of moldavites from sands involved a specific chemical differentiation which can not be explained by selective vaporization or melting, nor by selective condensation from melt or vapeur. Because large ions were enriched and small ones depleted in moldavites, the ionic radius has controlled the distribution of elements between sands and moldavites. We assume that moldavites originated from a plasma that the impact produced at its encounter with the surficial sand formation at the impact site, and that the primary units formed as early condensates in which large ions were preferentially trapped.