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.     

Simplified vibratory characterization of alluvial basins

For the analysis of seismic wave amplification, modal methods are interesting tools to study the modal properties of geological structures. Modal approaches mainly lead to information on such parameters as fundamental frequencies and eigenmodes of alluvial basins. For a specific alluvial deposit in Nice (France), a simplified modal approach involving the Rayleigh method is considered. This approach assumes a set of admissible shape functions for the eigenmodes and allows a fast estimation of the fundamental frequency of the basin. The agreement with other numerical results (Boundary Element Method) and experimental ones is fully satisfactory. The simplified modal method then appears as an efficient mean for the global vibratory characterization of geological structures towards resonance. To cite this article: J.-F. Semblat et al., C. R. Geoscience 335 (2003).     

轻质填充墙异型柱边框架抗震性能试验研究

本文重点研究了轻质填充墙异型柱边框架的层刚度衰减过程，承载力和弹塑性性能．     

新疆阿拉尔花岗岩MFC过程的微量元素综合效应

新疆阿拉尔花岗岩的微量元素比相关图显示了线性样点列与幂函数曲线形式的样点列相 复杂图型。该图型用简单混合或者单一结果分异模型都不能解释。本文建立了混合－结晶分异复合过程的微量元素综合效应模型。模型１：从初始混合线引起害虫函数曲线束形式的结晶分异线。特殊情况有结晶分异线简化为通过原点的直线束形式或者与初始混合线重合。     

JRC修正直边法的数学表达

JRC是反映爬坡角力学效应的岩体结构面表面形态等效描述指标。本文在爬坡角力学效应机理研究基础上, 阐述了JRC直边法的物理意义；通过岩体结构面表面起伏幅度与金属表面粗糙度幅度对比分析, 肯定了直边法的合理性；考虑JRC的尺寸效应, 推导JRC修正直边法的数学表达式, 编译计算机常用程序。最后, 实例检验了JRC修正直边法数学表达式的合理性和可用性。     

Application of an optimum design technique for determining the coefficient of consolidation by using piezocone test data

For normally consolidated clay, several researchers have developed a number of theoretical time factors to determine the coefficient of consolidation from piezocone test results. However, depending on assumptions and analytical techniques, it could vary considerably, even for a specific degree of consolidation. In this paper a method is proposed to determine a consistent coefficient of consolidation by applying the concept of an optimum design technique over all ranges of the degree of consolidation. Initial excess pore pressure distribution is assumed to be capable of being obtained by the successive spherical cavity expansion theory. The dissipation of pore pressure is simulated by means of a two-dimensional linear-uncoupled axi-symmetric consolidation analysis. The minimization of differences between measured and predicted excess pore pressure was carried out by the BFGS unconstrained optimum design algorithm with a one-dimensional golden section search technique. By analyzing numerical examples and in-situ test results, it was found that the adopted optimum design technique gives consistent and convergent results.     

Site effects at a vertical accelerometer array near Paducah, Kentucky

The downhole vertical accelerometer array VSAP near Paducah, KY, consists of three-component accelerometers at the surface, the top of the McNairy Formation (−41 m), and the top of the Paleozoic bedrock (—99 m). The array is at the northern end of the Mississippi Embayment, and it was installed to verify the ground-motion modeling for the site, assuming a significant earthquake in the New Madrid Seismic Zone. Accelerograms from 4.2 and 2.0 m_b earthquakes were used to check aspects of the modeling pertaining to linear behavior of the soil column, and to review the soil column models derived by drilling and geotechnical methods and through the use of high-resolution P- and SH-wave seismic refraction in reflection techniques. Results of the study indicate that for the linear case the soil column models derived by the two techniques are equivalent, and that the most important boundary in the soil column, with respect to amplification of the ground motions, is the interface between the limestone bedrock and soil.     

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.     

Use of microtremor measurement for assessing site effects in Northern Belgium – interpretation of the observed intensity during the MS = 5.0 June 11 1938 earthquake

To provide quantitative information on site effects in the northern part of Belgium, forty-seven H/V microtremor measurements were performed with 5 second seismometers over an area of about 15.000 km². Most of the results show a northward regular increase of the fundamental period in agreement with the augmentation of the Mesozoic and Cainozoic soft sedimentsthickness from a few meters 40 km south of Brussels to 900 m at the Netherlands-Belgium border. The measured resonance frequency values wereconsistent with theoretical computations performed at different sites onthe basis of existing information and shallow seismic experiments. At oneparticular site (Uccle) where borehole data were available, microtremor measurements using an array of four seismological stations with differentapertures allowed to obtain the low frequency part of the Rayleigh wave dispersion curve, extending the range covered by the analysis of surfacewaves artificially generated. The Vs profile derived from the surface waveinversion corroborates the 1 Hz natural frequency of the site. Comparison of these results with the macroseismic information concerning the M_S = 5.0 1938 earthquake which occurred 50 km west of Brussels,confirmed the hypothesis that the geological structure of the Brabant massifis likely to control damage distribution during such an earthquake. Comparisonbetween the intensity map of the 1938 earthquake and the resonance period ofsediments obtained by our microtremor study shows a clear relation betweenthe two parameters. During the 1938 earthquake, site effects played a prominent role due to the dimension of the source whose corner frequency wasabout 1 Hz.     

Approximate modal decomposition of inelastic dynamic responses of wall buildings

Two approximate methods for decomposing complicated inelastic dynamic responses of wall buildings into simple modal responses are presented. Both methods are based on the equivalent linear concept, where a non‐linear structure is represented by a set of equivalent linear models. One linear model is used for representing only one vibration mode of the non‐linear structure, and its equivalent linear parameters are identified from the inelastic response time histories by using a numerical optimizer. Several theoretical relations essential for the modal decomposition are derived under the framework of complex modal analysis. Various numerical examinations have been carried out to check the validity of the proposed modal decomposition methods, and the results are quite satisfactory in all cases. Fluctuating bending moment and shear at any location along the wall height contributed by each individual vibration mode can be obtained. Modal contributions to shear and flexural strength demands, as well as the corresponding modal properties, under various seismic loading conditions can also be identified and examined in detail. Furthermore, the effects of higher vibration modes on seismic demands of wall buildings are investigated by using the modal decomposition methods. Several new insights into the complicated inelastic dynamics of multi‐story wall buildings are presented. Copyright © 2004 John Wiley & Sons, Ltd.