Development of Winkler model for static and dynamic response of caisson foundations with soil and interface nonlinearities

As an extension of the elastic multi-spring model developed by the authors in a companion paper [Gerolymos N, Gazetas G. Winkler model for lateral response of rigid caisson foundations in linear soil. Soil Dyn Earthq Eng; 2005 (submitted companion paper).], this paper develops a nonlinear Winkler-spring method for the static, cyclic, and dynamic response of caisson foundations. The nonlinear soil reactions along the circumference and on the base of the caisson are modeled realistically by using suitable couple translational and rotational nonlinear interaction springs and dashpots, which can realistically (even if approximately) model such effects as separation and slippage at the caisson–soil interface, uplift of the caisson base, radiation damping, stiffness and strength degradation with large number of cycles. The method is implemented in a new finite difference time-domain code, NL-CAISSON. An efficient numerical methodology is also developed for calibrating the model parameters using a variety of experimental and analytical data. The necessity for the proposed model arises from the difficulty to predict the large-amplitude dynamic response of caissons up to failure, statically or dynamically. In a subsequent companion paper [Gerolymos N, Gazetas G. Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results. Soil Dyn Earthq Eng; 2005 (submitted companion paper).], the model is validated against in situ medium-scale static load tests and results of 3D finite element analysis. It is then used to analyse the dynamic response of a laterally loaded caisson considering soil and interface nonlinearities.     

Winkler model for lateral response of rigid caisson foundations in linear soil

A generalized spring multi-Winkler model is developed for the static and dynamic response of rigid caisson foundations of circular, square, or rectangular plan, embedded in a homogeneous elastic. The model, referred to as a four-spring Winkler model, uses four types of springs to model the interaction between soil and caisson: lateral translational springs distributed along the length of the caisson relating horizontal displacement at a particular depth to lateral soil resistance (resultant of normal and shear tractions on the caisson periphery); similarly distributed rotational springs relating rotation of the caisson to the moment increment developed by the vertical shear tractions on the caisson periphery; and concentrated translational and rotational springs relating, respectively, resultant horizontal shear force with displacement, and overturning moment with rotation, at the base of the caisson. For the dynamic problem each spring is accompanied by an associated dashpot in parallel. Utilising elastodynamic theoretical available in the literature results for rigid embedded foundations, closed-form expressions are derived for the various springs and dashpots of caissons with rectangular and circular plan shape. The response of a caisson to lateral static and dynamic loading at its top, and to kinematically-induced loading arising from vertical seismic shear wave propagation, is then studied parametrically. Comparisons with results from 3D finite element analysis and other available theoretical methods demonstrate the reliability of the model, the need for which arises from its easy extension to multi-layered and nonlinear inelastic soil. Such an extension is presented in the companion papers by the authors [Gerolymos N, Gazetas G. Development of Winkler model for lateral static and dynamic response of caisson foundations with soil and interface nonlinearities. Soil Dyn Earthq Eng. Submitted companion paper; Gerolymos N, Gazetas G. Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results. Soil Dyn Earthq Eng. Submitted companion paper.].     

The Third Integral in a Self-consistent Galactic Model

We apply the theory of the third integral to a self-consistent galactic model, generated by the collapse of a N-body system. The final configuration after the collapse is a stationary triaxial system, that represents an almost prolate non-rotating elliptical galaxy with its longest axis in the z-direction. This system is represented by an axisymmetric potential V plus a small triaxial perturbation V ₁. The orbits in the potential V are of three types: box orbits, tube orbits (corresponding to various resonances), and chaotic orbits.The intersections of the box and tube orbits by a Poincaré surface of section z=0 are closed invariant curves. The main tube orbits are like ellipses and form an island of stability on the (R,R) plane.We calculated the third integral I in the potential V for the general non-resonant case and for various resonant cases. The agreement between the invariant curves of the orbits and the level curves of the third integral is good for the box and tube orbits, if we truncate the third integral at an appropriate level. As expected the third integral fails in the case of chaotic orbits. The most important result is the form of the number density F on the Poincaré surface of section. This function decreases exponentially outwards for the box orbits, like Fexp(–bI), while it is constant, as expected, for the chaotic orbits. In the case of the island of the main tube orbits it has a minimum at the center of the island. This can be explained by the form of the near elliptical orbits that are elongated along R, thus they fail to support a self-consistent galaxy, which is elongated along the z-axis.     

Assessment of natural and anthropogenic impacts in groundwater,utilizing multivariate statistical analysis and inverse distance weighted interpolation modeling: the case of a Scopia basin (Central Greece)

In Scopia basin, central Greece, a hydrochemical investigation was completed. Groundwater samples from 41 sites were used to assess the natural and anthropogenic impacts in groundwater, utilizing the principal component analysis (PCA) involved with the inverse distance weighted (IDW) interpolation modeling and hierarchical cluster analysis (HCA). Best fit model to explain the spatial distribution of both hydrochemical parameters and PCA was chosen by optimizing the IDW interpolator’s parameters. Precision of the model was picked based on less root-mean-squared prediction error (RMSPE) amongst predicted and actual values measured at the same locations. Groundwater exhibit Ca–Mg–HCO₃ as the dominant hydrochemical type and their greater part are mixed waters with non-dominant ion. Interpolation models demonstrate high estimations of nitrates in zones with agricultural activities and high estimations of nickel and chromium in regions with the strong presence of ultrabasic rocks. Dominant part of the groundwater samples surpasses in many cases the European Community (EC) drinking water permissible limits. Thus, they are unsuitable for human consumption. PCA illustrated four factors, which clarified 80.62% of the aggregate variance of data and HCA classified two statistically significant clusters of sampling sites. Results show natural procedures ascribed to the weathering of the minerals contained in the ultrabasic rocks and anthropogenic influences related to the use of fertilizers and wastewater leak. In light of FAO standards and Richards’s classification, the groundwaters are reasonable for irrigation purposes, featuring waters with low sodium hazard and moderate salinity hazard.     

Counterrotating Galaxies and Memory of Cosmological Initial Conditions

As it is known, a good number of galaxies are observed to have counterrotating cores. A popular scenario to explain the formation of such galaxies is based on a secondary process of merging of galaxies with their satellites, or gas infall, or merger events between galaxies. An alternative mechanism, proposed by Voglis et al., 1991, and by Harsoula and Voglis 1998, could also be responsible for the formation of these galaxies directly from cosmological initial conditions (direct scenario). The novel mechanism was demonstrated by using quiet cosmological initial conditions in N-body simulations. In the present paper we extend our N-body simulations using clumpy initial conditions and show that this mechanism still works to create counterrotating galaxies. Counterrotation is a result of the considerable amount of memory of initial conditions surviving for times comparable to the Hubble time, despite the large degree of instability of individual orbits and the dramatic redistribution and mixing of the particles in phase space. We show, for example, that the particles remember, in a statistical sense, not only their distance from the center of mass (memory of energy), but also the initial orientation of their position relative to the direction of an external tidal field, which determines the sign and the amount of angular momentum that is transferred to the particles of the system.     

Seismic design of RC structures: A critical assessment in the framework of multi‐objective optimization

The assessment of seismic design codes has been the subject of intensive research work in an effort to reveal weak points that originated from the limitations in predicting with acceptable precision the response of the structures under moderate or severe earthquakes. The objective of this work is to evaluate the European seismic design code, i.e. the Eurocode 8 (EC8), when used for the design of 3D reinforced concrete buildings, versus a performance‐based design (PBD) procedure, in the framework of a multi‐objective optimization concept. The initial construction cost and the maximum interstorey drift for the 10/50 hazard level are the two objectives considered for the formulation of the multi‐objective optimization problem. The solution of such optimization problems is represented by the Pareto front curve which is the geometric locus of all Pareto optimum solutions. Limit‐state fragility curves for selected designs, taken from the Pareto front curves of the EC8 and PBD formulations, are developed for assessing the two seismic design procedures. Through this comparison it was found that a linear analysis in conjunction with the behaviour factor q of EC8 cannot capture the nonlinear behaviour of an RC structure. Consequently the corrected EC8 Pareto front curve, using the nonlinear static procedure, differs significantly with regard to the corresponding Pareto front obtained according to EC8. Furthermore, similar designs, with respect to the initial construction cost, obtained through the EC8 and PBD formulations were found to exhibit different maximum interstorey drift and limit‐state fragility curves. Copyright © 2007 John Wiley & Sons, Ltd.     

A forward/backward principal component analysis of Landsat-7 ETM+ data to enhance the spectral signal of burnt surfaces

In this paper, principal component analysis (PCA), a dimensionality reduction method, has been applied successfully as an image enhancement technique to improve the spectral signal of burnt surfaces. Forward/backward PCA (F/B PCA) and image differencing, which the proposed method consists of, creates a new spectral space that preserves the original spectral patterns while enhancing particular structures of the original satellite data. Burnt surfaces constitute a spectrally enhanced feature after selective removal of spectral information from the original Landsat-7 Enhanced Thematic Mapper data.Improvement of the spectral separability of burnt surfaces is most evident in spectral channels ETM+4 and ETM+7, where burnt surfaces already compose distinct spectral objects, and channels ETM+2 and ETM+5. This improvement is reasonable since the third PC axis, which is not considered in the back-transformation, is composed mainly of the spectral information in these channels. Another benefit of the technique is a reduction of interband correlation in the satellite data.No clear differences between the standardized and non-standardized F/B PCA were identified to recommend the use of one over the other. Both methods show advances in certain aspects. Finally, an increase of the separability value between burnt areas and dry vegetated areas from 0.473 to 1.06 and 1.31 was obtained with the use of the standardized and non-standardized F/B PCA, respectively.     

Rockshelter sedimentation in a dynamic tropical landscape: Late Pleistocene–Early Holocene archaeological deposits in Kitulgala Beli‐lena,southwestern Sri Lanka

Kitulgala Beli‐lena, a rockshelter in gneiss in humid tropical southwestern Sri Lanka, was inhabited by Late Pleistocene–Early Holocene (>31,000–7880 B.P.) hunter‐gatherers who made geometric microliths and exploited rainforest resources. Micromorphological analysis of a ca. 3‐m‐thick succession of diamictic loams, clays, and breccia with cultural content suggests that relative contribution of episodic colluviation and roof fall, water seepage through joints and diverse human activity varied through time. Facies changes across the profile reflect monsoon weakening ca. 20,000–16,000 cal B.P. and abrupt intensification ca. 15,700 cal B.P., on the wane of the global Last Glacial Maximum (LGM). Post‐depositional modification included clay, sesquioxide, and minor phosphate translocation; termite and other arthropod bioturbation; and clast weathering on the rockshelter floor. Human input (tools and tool‐making refuse, reworked charcoal and associated combustion by‐products) is markedly higher in sediments younger than ca. 15,700 cal B.P., suggesting intensification of site use immediately after the LGM. © 2009 Wiley Periodicals, Inc.