Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations

The paper provides state-of-the-art information on the following aspects of seismic analysis and design of spread footings supporting bridge piers: (1) obtaining the dynamic stiffness (“springs” and “dashpots”) of the foundation; (2) computing the kinematic response; (3) determining the conditions under which foundation–soil compliance must be incorporated in dynamic structural analysis; (4) assessing the importance of properly modeling the effect of embedment; (5) elucidating the conditions under which the effect of radiation damping is significant; (6) comparing the relative importance between kinematic and inertial response. The paper compiles an extensive set of graphs and tables for stiffness and damping in all modes of vibration (swaying, rocking, torsion), for a variety of soil conditions and foundation geometries. Simplified expressions for computing kinematic response (both in translation and rotation) are provided. Special issues such as presence of rock at shallow depths, the contribution of foundation sidewalls, soil inhomogeneity and inelasticity, are also discussed. The paper concludes with parametric studies on the seismic response of bridge bents on embedded footings in layered soil. Results are presented (in frequency and time domains) for accelerations and displacements of bridge and footing, while potential errors from some frequently employed simplifications are illustrated.     

Refinement of the modified time-to-failure method for intermediate-term earthquake prediction

The modified time-to-failure method for intermediate-term earthquake prediction utilizes empirical relationships to reduce the number of unknown parameters providing a stable and unique solution set. The only unknown parameters in the modified time-to-failure method are the time and size of the impending main shock. The modified time-to-failure equation is used to model the precursory events and a prediction contour diagram is constructed with the magnitude and time-of-failure as the axes of the diagram. The root-mean-square (rms) is calculated for each set of time and magnitude on the prediction diagram representing the difference between the model (calculated) acceleration and the actual accelerated energy release of the precursory events. A small region, corresponding to the low rms region on the diagram, defines the prediction. The prediction has been shown to consistently under-estimate the magnitude and over-estimate the time-of-failure. These shortcomings are caused by an underestimation in energy release of the modified time-to-failure equation at the very end of the sequence. An empirical correction can be applied to the predicted results to minimize this problem. A main shock location search technique has been developed for use with the modified time-to-failure method. The location technique is used to systematically search an earthquake catalog and identify locations corresponding to precursory sequences that display accelerated energy releases. It has shown good results when applied in retrospective predictions, and is essential for the practical application of the modified time-to-failure method. In addition, an observed linear characteristic in long-term energy release can be used to minimize false predictions. The refined empirical relationships that eliminate or constrain unknown constants used in the modified time-to-failure method and the main shock location search technique are used in a practical application in the New Madrid Seismic Zone (NMSZ). The NMSZ, which is over due for a magnitude 6 event according to recurrence rates (Johnston and Nava, 1985), makes this region ideal for testing the method. One location was identified in the NMSZ as a high risk area for an event in the magnitude 4.5 range. The prediction, if accurate, is of scientific interest only because of the relatively small size of the main shock.     

Nature and significance of the Neoproterozoic Sturtian–Marinoan Boundary,Northern Adelaide Geosyncline,South Australia

The Cryogenian succession of the Northern Flinders Ranges reveals a complex sedimentary record between the Sturtian and Marinoan glacial deposits. A major unconformity separates the Sturtian and Marinoan-aged sedimentary successions in the area. This forms a subaerial erosion surface with terrestrial and marginal marine infill directly above the Angepena and Balcanoona Formations in their respective localities. This exposure surface is here correlated with the previously documented submarine unconformity between the Yankaninna Formation and the underlying deep marine Tapley Hill Formation. This erosional event provides a chronostratigraphic marker horizon that coincides approximately with thepreviously defined Sturtian–Marinoan Time Series boundary in the Northern Flinders Ranges. These stratigraphic relationships also constrain lateral facies relationships between the Oodnaminta ReefComplex (Balcanoona Formation) and the Angepena Formation. Similarly, the shallow-water Weetootla Dolomite is correlated with the deeper water carbonates of the Yankaninna Formation.     

Solar rotation, 1966–1978

Photospheric and chromospheric spectroscopic Doppler rotation rates for the full solar disk are analyzed for the period July, 1966 to July, 1978. An approximately linear secular increase of the equatorial rate of 3.7% for these 12 years is found (in confirmation of Howard, 1976). The high latitude rates above 65 ° appear to vary with a peak-to-peak amplitude of 8%, or more, phased to the sunspot cycle such that the most rapid rotation occurs at, or following, solar maximum. The chromosphere, as indicated by H, has continued to rotate on the average 3% faster than the photosphere agreeing with past observations. Sources of error are discussed and evaluated.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Oceanic versus island arc origin of ophiolites

The silica content of basaltic rocks is an unreliable variable with which to distinguish ultramafic-mafic complexes developed at ocean ridges from those potentially formed beneath volcanic island arcs. Data from Appalachian ophiolites supports the view that silica metasomatism is responsible for the high silica content of supposed calc-alkaline basaltic rocks found in ophiolites such as Troodos, and that the high-silica (70 wt.%) leucocratic rocks associated with ophiolites are of tholeiitic rather than calc-alkaline parentage. The use of titanium as a discriminant of tectonic environment is also suspect because the titanium content of basalts associated with Appalachian ophiolites as well as those recently recovered from the Atlantic ocean floor ranges from values even lower than those typical of island arc tholeiites to values typical of abyssal tholeiites. However, the internal stratigraphy of ophiolites in both the Appalachian and Tethyan systems can only be explained on the basis of the postulate that ophiolites originate at oceanic spreading centres rather than beneath island arcs.     

The effect of cracks on the thermal expansion of rocks

Thermal expansion during the first heating cycle at atmospheric pressure was measured in several directions in seven igneous rocks between 25° and 400°C at slow heating rates. The coefficient of thermal expansion measured under these conditions increases more rapidly as temperature is increased than the average thermal expansion coefficient of the constituent minerals. The “extra” expansion is attributed to the formation of cracks by differential expansion of mineral grains. The presence of such cracks in the rocks during the cooling part of the cycle and during any subsequent heating and cooling cycles will result in a substantial decrease in the coefficient of thermal expansion as compared to that measured during the first heating cycles. The effect of cracks initially present in a rock was studied by measuring the full tensor of the coefficient of thermal expansion on two rocks with anisotropic crack distributions. In these two rocks the coefficient of thermal expansion is least in the direction perpendicular to the plane of greatest crack concentration. The implication of our data is that thermal expansion depends greatly on the fracture state of the rock. Both the fractures in the rock and the boundary conditions on the rock are significant for the interpretation of thermal expansion measurements and for their application to other problems.     

On the Principle of Least Interaction Action and the Laplacean satellites of Jupiter and Uranus

The Principle of Least Interaction Action, which explains the observed preference in the Solar System for two-satellite resonant configurations, is shown to apply also to the Laplacean satellites of Jupiter and Uranus, in the sense that these triplet resonant structures lie close to configurations for which the time-mean of the action associated with the mutual interaction of the satellites is an overall minimum. Far from the minimum configuration, significant changes take place in the major semi-axes on time-scales ～10⁶-10⁷y. Both systems require times ～10⁸ y to come close to the minimum configuration; to approach resonance to the observed precision of the Laplace relationship (3×10^?4 for the Uranian case, 2×10^?7 for the Jovian case) requires, for both systems, a time closely comparable with the age of the solar system.