Non‐stationary seismic response of tanks with soil interaction by wavelets

A wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.     

Influence of seismic motions on behavior of piles in liquefied soils

In the present study an analytical procedure based on finite element technique is proposed to investigate the influence of vertical load on deflection and bending moment of a laterally loaded pile embedded in liquefiable soil, subjected to permanent ground displacement. The degradation of subgrade modulus due to soil liquefaction and effect of nonlinearity are also considered. A free headed vertical concrete elastic nonyielding pile with a floating tip subjected to vertical compressive loading, lateral load, and permanent ground displacement due to earthquake motions, in liquefiable soil underlain by nonliquefiable stratum, is considered. The input seismic motions, having varying range of ground motion parameters, considered here include 1989 Loma Gilroy, 1995 Kobe, 2001 Bhuj, and 2011 Sikkim motions. It is calculated that maximum bending moment occurred at the interface of liquefiable and nonliquefiable soil layers and when thickness of liquefiable soil layer is around 60% of total pile length. Maximum bending moment of 1210 kNm and pile head deflection of 110 cm is observed because of 1995 Kobe motion, while 2001 Bhuj and 2011 Sikkim motions amplify the pile head deflection by 14.2 and 14.4 times and bending moment approximately by 4 times, when compared to nonliquefiable soil. Further, the presence of inertial load at the pile head increases bending moment and deflection by approximately 52% when subjected to 1995 Kobe motion. Thus, it is necessary to have a proper assessment of both kinematic and inertial interactions due to free field seismic motions and vertical loads for evaluating pile response in liquefiable soil.     

Distribution of stars perpendicular to the plane of the galaxy

We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m₀)m^−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v²(m)> ∼ m^−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field K_z, in terms of confluent hypergeometric functions, the limiting trends being K_z∼z for z →0, while K_z → constant for z → infinity. We also study the behaviour of < |z(m)|²>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|²>∼ m^t-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested that observation of < |z(m)|²> can be used as a probe to findx and hence obtain information about the mass spectrum.     

Energy dissipation in wave propagation in general-relativistic plasma

Based on a recent communication by the present authors the question of energy dissipation in magnetohydrodynamical waves in an inflating background in general relativity is examined. It is found that the expanding background introduces a sort of dragging force on the propagating wave such that, unlike the Newtonian case, energy gets dissipated as it progresses. This loss in energy having no special-relativistic analogue is, however, not mechanical in nature as in case of an elastic wave. It is also found that the energy loss is model dependent and also depends on the number of dimensions.     

Thermodynamic mixing properties of Mg(Al,Cr)2O4 spinel crystalline solution at high temperatures and pressures

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies. Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, and . The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: , P expressed in bars, T in K, G _m ^ex and W _G,i ^Sp in joules/mol. Temperature-dependence of G _m ^ex is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 , and changes barely with pressure. Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.     

Dynamical Initialization of Boundary-Layer Data

A procedure for the dynamic initialization of wind and temperature fields within the atmospheric boundary layer (ABL) is presented. The procedure uses transilient turbulence theory to assess the turbulent fluxes from observed wind and temperature data, which are used to estimate the eddy transfer coefficients, so enabling a local closure ABL model to be integrated forward in time to a new steady state. The method has been applied to initialize kytoon data taken at Kharagpur (22.3° N, 87.2° E) during the MONTBLEX field programme. Results of a case study for 17 June 1990 are discussed.     

Exploring Granger causality between global average observed time series of carbon dioxide and temperature

Detection and attribution methodologies have been developed over the years to delineate anthropogenic from natural drivers of climate change and impacts. A majority of prior attribution studies, which have used climate model simulations and observations or reanalysis datasets, have found evidence for human-induced climate change. This papers tests the hypothesis that Granger causality can be extracted from the bivariate series of globally averaged land surface temperature (GT) observations and observed CO₂ in the atmosphere using a reverse cumulative Granger causality test. This proposed extension of the classic Granger causality test is better suited to handle the multisource nature of the data and provides further statistical rigor. The results from this modified test show evidence for Granger causality from a proxy of total radiative forcing (RC), which in this case is a transformation of atmospheric CO₂, to GT. Prior literature failed to extract these results via the standard Granger causality test. A forecasting test shows that a holdout set of GT can be better predicted with the addition of lagged RC as a predictor, lending further credibility to the Granger test results. However, since second-order-differenced RC is neither normally distributed nor variance stationary, caution should be exercised in the interpretation of our results.     

In-cloud and below-cloud scavenging of aerosol ionic species over a tropical rural atmosphere in India

The temporal variation in concentrations of major water soluble ionic species has been studied from several rain events occurred over Gadanki (13.5 °N, 79.2 °E), located in tropical semi arid region in southern India. The contribution from rain-out (in cloud) and wash-out (below cloud) processes to the total removal of ionic species by rain events is also estimated using the pattern of variations of ionic species within an individual event. A number of rain samples were collected from each rain event during June–November in 2006, 2007 and 2008. On average, nearly 20% of the total NH ₄ ⁺ and non-sea SO ₄ ^2? is removed by in-cloud scavenging, suggesting that their removal by “below cloud” washout is relatively dominant. In contrast Na⁺, Ca²⁺, Mg²⁺, NO ₃ ^? and sea-SO ₄ ^2? are mainly removed by below-cloud scavenging or wash-out process. A significant variation in the acidity was observed within rain events with successive precipitation showing higher acidity at the final stage of the precipitation due to partial neutralization of non-sea SO ₄ ^2? . Overall, greater influence of both terrestrial and anthropogenic sources is recorded in the rain events compared to that from marine sources.     

Variations in shear wave velocity and soil site class in Kolkata city using regression and sensitivity analysis

The detrimental effects of an earthquake are strongly influenced by the response of soils subjected to dynamic loading. The behavior of soils under dynamic loading is governed by the dynamic soil properties such as shear wave velocity, damping characteristics and shear modulus. Worldwide, it is a common practice to obtain shear wave velocity (V _s in m/s) using the correlation with field standard penetration test (SPT) N values in the absence of sophisticated dynamic field test data. In this paper, a similar but modified advanced approach has been proposed for a major metro city of eastern India, i.e., Kolkata city (latitudes 22°20′N–23°00′N and longitudes 88°04′E–88°33′E), to obtain shear wave velocity profile and soil site classification using regression and sensitivity analyses. Extensive geotechnical borehole data from 434 boreholes located across 75 sites in the city area of 185 km² and laboratory test data providing information on the thickness of subsoil strata, SPT N values, consistency indices and percentage of fines are collected and analyzed thoroughly. A correlation between shear wave velocity (V _s) and SPT N value for various soil profiles of Kolkata city has been established by using power model of nonlinear regression analysis and compared with existing correlations for other Indian cities. The present correlations, having regression coefficients (R ²) in excess of 0.96, indicated good prediction capability. Sensitivity analysis predicts that significant influence of soil type exists in determining V _s values, for example, typical silty sand shows 30.4 % increase in magnitude of V _s as compared to silt of Kolkata city. Moreover, the soil site classification shows Class D and Class E category of soil that exists typically in Kolkata city as per NEHRP (Recommended provisions for seismic regulations for new buildings and other structures—Part 1: Provisions. Prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency (Report FEMA 450), Washington, DC, 2003) guidelines and thereby highlighting the seismic vulnerability of the city. The results presented in this study can be utilized for seismic microzonation, ground response analysis and hazard assessment for Kolkata city.

     

Lead isotope and trace element composition of K-feldspars from peraluminous granitoids of the Late Devonian South Mountain Batholith (Nova Scotia, Canada): implications for petrogenesis and tectonic reconstruction

The South Mountain Batholith (SMB) of southwestern Nova Scotia (Canada) is a Late Devonian (~375 Ma) composite intrusion, which crops over an area of about 7,300 km². This peraluminous granitoid body consists of rocks ranging from granodiorite through monzogranite and leucomonzogranite to leucogranite that locally host greisen tin-base metal mineralization. K-feldspar displays large compositional variations of trace elements and Pb isotopic ratios, particularly in the highly fractionated rocks. Many variations are consistent with processes of fractional crystallization, but a distinct enrichment of Rb, Li and Cs accompanied by low K/Rb, Ba/Rb, Eu/Eu* and K/Cs ratios point to the role of fluids during the late stages of magmatic evolution. The correlation of Pb isotopic ratios with the enriched elements and their ratios implies that the isotopic variations are an integral part of the evolution of the SMB. Together with well-defined isochronal relationships of Pb systems in the feldspars, the correlation suggests that fractional crystallization accompanied in the late stages by fluid fractionation led to the formation of Li–F-rich leucogranites. Internally derived U-rich fluids fractionated U/Pb ratios, which in turn produced distinct variations of ²⁰⁶Pb/²⁰⁴Pb and ²³⁸U/²⁰⁴Pb ratios in K-feldspars. This implies that the Pb isotopic values of K-feldspar, which have traditionally been used for tectonic reconstructions, might have been modified in many granitic rocks. Thus, only early magmatic K-feldspars, which show no discernible effects of fluid fractionation yield the initial Pb isotopic compositions of the parental granitic magmas and their sources. The data also show that the geochemical characteristics of the leucogranites are the results of magmatic evolution rather than a distinctive source.