Principal axes of m-DOF structures PartⅠ:Static loading

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems,and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading.This first paper deals with quantitative definitions of principal axes and "cross effects" of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part Ⅱ of this series.     

Modeling of Rayleigh waves dispersion in the Sannio region (Southern Italy) from seismic active refraction data

Short period surface waves, recorded during a seismic refractionsurvey in the Sannio region (Southern Italy), have been modeled to infera shallow velocity model for the area. Based on the decrease of resolutionwith depth, due to the bias on group velocity estimates arising frominterference of the Rayleigh waves with higher modes, we carried out aprocedure of fitting, with synthetic seismograms, of selected filtered traceswith a gaussian filter, having a width at half height equal to 1 Hz and acentral frequency lying in the range [1,4] Hz. We estimated the likelihoodbetween synthetic and observed seismograms by measuring their semblance.In this way we were able to infer a more refined local velocity modelcharacterized by a high Vp and Vs vertical gradient in the sedimentarycover. Two ad hoc resolution studies, based on group velocity andamplitude data respectively, indicate that the local velocity model is a goodvelocity model also for the entire studied area. The increase in the numberof available data when using amplitude information allows us to make amore selective choice in the model parameter space (Vp and Vs of eachlayer) and to solve for the Vp/Vs ratio. The inferred Vp velocity in thehalf-space is equal to 2.8 km/s. This value is in excellent agreement withthat inferred by other authors (3 km/s) by modeling P-wave travel timevs. distance. The best-fit model furnish low Vp/Vs for the sedimentarycover so indicating a high degree of the sediment's compaction in thestudied area. The inferred shallow high-velocity gradient indicates thatthe shallow sedimentary layer in the area could trap and focus the energytraveling into it.     

A hybrid indirect boundary element—discrete wave number method applied to simulate the seismic response of stratified alluvial valleys

A hybrid indirect boundary element – discrete wavenumber method is presented and applied to model the ground motion on stratified alluvial valleys under incident plane SH waves from an elastic half-space. The method is based on the single-layer integral representation for diffracted waves. Refracted waves in the horizontally stratified region can be expressed as a linear superposition of solutions for a set of discrete wavenumbers. These solutions are obtained in terms of the Thomson–Haskell propagators formalism. Boundary conditions of continuity of displacements and tractions along the common boundary between the half-space and the stratified region lead to a system of equations for the sources strengths and the coefficients of the plane wave expansion. Although the regions share the boundary, the discretization schemes are different for both sides: for the exterior region, it is based on the numerical and analytical integration of exact Green's functions for displacements and tractions whereas for the layered part, a collocation approach is used. In order to validate this approach results are compared for well-known cases studied in the literature. A homogeneous trapezoidal valley and a parabolic stratified valley were studied and excellent agreement with previous computations was found. An example is given for a stratified inclusion model of an alluvial deposit with an irregular interface with the half-space. Results are displayed in both frequency and time domains. These results show the significant influence of lateral heterogeneity and the emergence of locally generated surface waves in the seismic response of alluvial valleys.     

ADV measurements of velocity distributions in a gravel‐bed flume

Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d₈₄, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Time-domain computation of scattering from a heterogeneous layer

Adopting Born and ray approximations, time-domain synthetic seismograms for P-P and P-S scattering from a plane wave incident on a thin, laterally heterogeneous layer are presented in this paper. The time-domain P coda is a convolution between a structure function and the second-order derivative of the time function of the incident P wave. Examples of synthetic seismograms are given using a time function from a computed short-period seismogram for a point explosive source in a half-space. These show that it is impossible, with realistic values of the parameters involved, to generate significant codas when only single scattering is involved.     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.     

Estimation of Site Effects in Beijing City

— For the realistic modeling of the seismic ground motion in lateral heterogeneous anelastic media, the database of 3-D geophysical structures for Beijing City has been built up to model the seismic ground motion in the City, caused by the 1976 Tangshan and the 1998 Zhangbei earthquakes. The hybrid method, which combines the modal summation and the finite-difference algorithms, is used in the simulation. The modeling of the seismic ground motion, for both the Tangshan and the Zhangbei earthquakes, shows that the thick Quaternary sedimentary cover amplifies the peak values and increases the duration of the seismic ground motion in the northwestern part of the City. Therefore the thickness of the Quaternary sediments in Beijing City is the key factor controling the local ground effects. Four zones are defined on the base of the different thickness of the Quaternary sediments. The response spectra for each zone are computed, indicating that peak spectral values as high as 0.1 g are compatible with past seismicity and can be well exceeded if an event similar to the 1697 Sanhe-Pinggu occurs.