Consistent formulation of direct and substructure methods in nonlinear soil-structure interaction

Both direct and substructure methods of dynamic soil-structure interaction analysis can be treated using a common analytical model with difference being restricted only to the definition of boundary conditions of the bounded soil zone. It is shown that a consistent formulation of the problem equally applicable to both methods can be achieved in which true nonlinear behaviour of the bounded soil zone (near-field) can be taken into account in the time domain through properly defined constitutive models. However, for the linear boundary conditions to be imposed on the near-field inevitably involves the application of the principle of superposition resulting in a linear far-field approximation. Therefore, the bounded soil zone taken should be large enough in both methods to reduce the adverse effects of the far-field linearization.     

Coupling of boundary and finite elements for soil-structure interaction problems

The investigation of complex soil-structure interaction problems is usually carried out with numerical solution procedures such as the finite element or the boundary element method. It must be noted, however, that the choice of one or the other of these approaches is not just a matter of preferences; depending on the type of the problem under consideration, either boundary or finite elements may be more advantageous. A considerable expansion in the computational power can be obtained, on the other hand, if one resorts to hybrid schemes which retain the main advantages of the two methods and eliminate their respective disadvantages. This paper presents results obtained with a boundary element-finite element coupling procedure, and discusses its applicability to some representative soil-structure interaction problems. The structures considered are elastic systems, such as foundations, tunnels and filled trenches (modelled by finite elements), which are coupled with homogeneous elastic halfspaces (modelled by boundary elements). The examples demonstrate the importance of using a model that includes wave radiation effects. The coupling approach is formulated entirely in the time domain so that an extension of the algorithm to non-linear analyses seems to present no further difficulties.     

土-结构相互作用地震反应分析软件及其二次开发

本文简要介绍了目前在土-结构相互作用分析中常用的有限元软件ANSYS7.0、FLAC和MSC.M arc,通过比较评价其各自优缺点和适用性后,根据高层建筑结构土-结构相互作用地震反应分析的特点,建议利用带有灵活接口的大型非线性有限元分析软件MSC.M arc作为其分析工具,并尝试对MSC.M arc进行二次开发,将多层土E-B本构关系模型作为子程序加入其中。     

A plane strain soil-structure interaction model

A plane strain model for dynamic soil-structure interaction problems under harmonic state is presented. The boundary element method is used to study the response of a homogeneous isotropic linear elastic soil. The far field displacement at the free surface is approximated by an outgoing Rayleigh wave. The finite element method is used to describe the response of the building, of the foundation and possibly of a finite part of the inhomogeneous non-linear soil. Two coupling procedures are described. The model is applied to a problem previously studied in the antiplane case. Incident P, SV and Rayleigh waves are considered. The results show an amplification and an attenuation of the structure motion with frequency when incident Rayleigh waves and P, SV body waves are respectively considered.     

Elastodynamic boundary element formulation employing discontinuous curved elements

A boundary element formulation having discontinuous curved quadratic elements is presented for 2D elastodynamics. The first fundamental solution for static case is subtracted from and added to the first fundamental solution for dynamic case. As both kernels have the same order of singularity, the integral involving the regular expression arising from the subtraction can be calculated. matrix is calculated by employing the well-known rigid-body motion technique. The formulation is performed in Fourier transform space. Based on the formulation presented in this study, a general purpose computer program is developed for elastic or visco-elastic 2D elastodynamic problems. The program performs the analysis in Fourier transform space and can also be used for static analysis by assigning a very small value close to zero for the frequency. The results of some elastodynamic and dynamic soil–structure interaction problems obtained using the present study are compared with those in the literature.     

Doppler effect in high-speed rail seismic wavefield and its application

We demonstrate by theoretical analysis that periodically distributed viaduct piers of high-speed rail result in the Doppler effect in the seismic wavefield of high-speed rail at specific frequencies and analyze the Doppler effect’s influence on the wavefield’s spectrum feature.We further verify our theoretical prediction by using observational data of the high-speed rail seismic wavefield in Rongcheng,Hebei Province,China.We find that the wavefield component with a noticeable Doppler effect vibrates in the propagation direction and only has a unique apparent wave speed,indicating that P-wave is dominant.Furthermore,we propose a speed measurement method based on the Doppler effect and measure the wave speed of the medium along the rail.Measurement results are highly stable and consistent.     

Filter formulation and wavefield separation of cross-well seismic data

Multichannel filtering to obtain wavefield separation has been used in seismic processing for decades and has become an essential component in VSP and cross-well reflection imaging. The need for good multichannel wavefield separation filters is acute in borehole seismic imaging techniques such as VSP and cross-well reflection imaging, where strong interfering arrivals such as tube waves, shear conversions, multiples, direct arrivals and guided waves can overlap temporally with desired arrivals. We investigate the effects of preprocessing (alignment and equalization) on the quality of cross-well reflection imaging wavefield separation and we show that the choice of the multichannel filter and filter parameters is critical to the wavefield separation of cross-well data (median filters, f–k pie-slice filters, eigenvector filters). We show that spatial aliasing creates situations where the application of purely spatial filters (median filters) will create notches in the frequency spectrum of the desired reflection arrival. Eigenvector filters allow us to work past the limits of aliasing, but these kinds of filter are strongly dependent on the ratio of undesired to desired signal amplitude. On the basis of these observations, we developed a new type of multichannel filter that combined the best characteristics of spatial filters and eigenvector filters. We call this filter a ‘constrained eigenvector filter’. We use two real data sets of cross-well seismic experiments with small and large well spacing to evaluate the effects of these factors on the quality of cross-well wavefield separation. We apply median filters, f–k pie-slice filters and constrained eigenvector filters in multiple domains available for these data sets (common-source, common-receiver, common-offset and common-midpoint gathers). We show that the results of applying the constrained eigenvector filter to the entire cross-well data set are superior to both the spatial and standard eigenvector filter results.     

考虑相邻结构影响的土-结构动力相互作用研究综述

对相邻结构动力相互作用(DCI)的研究历史与现状作了回顾和介绍,将其发展过程分为三个阶段,并对各时期发展的主要内容和特点进行了概述,最后对该领域今后的研究趋势作了分析。     

Thin layer element method for dynamic soil-structure interaction analysis of axi-symmetric structure in submerged soil

The three-dimensional thin layer element method is formulated for the dynamic response analysis of an axi-symmetric structure in submerged soil. Biot's wave equation for fluid-filled porous medium is used in the formulation. The three-dimensional thin layer element method computes the wave numbers and their associated mode shapes, for both Rayleigh waves and Love waves in submerged soil, which define the characteristics of the waves. The submerged condition affects the characteristics of the Rayleigh waves in soil. As a result, it alters substantially the soil-structure interaction stresses if the permeability of the soil is relatively large and, to less extent, the response of the structure. The thin layer element method is far more efficient than the finite element method for analyzing the fluid-filled porous medium, yet capable of taking into account a multi-layered inhomogeneous soil.     

A modified lumped parametric model for nonlinear soil-structure interaction analysis

Most soil—structure interaction (SSI) analyses are still conducted assuming linear material behavior or simulating nonlinear effects through an equivalent linearization and the structure (foundation) being closely welded with the surrounding soil. It is recognized, however, that nonlinearities can play a significant role in the results. Two kinds of nonlinearities must be considered: those associated with inelastic soil behavior and those resulting from loss of contact between the foundation and the surrounding soil. In the present paper a modified lumped parametric model for the analysis of nonlinear SSI effects has been proposed. In the model both nonlinearities are taken into account. The results of tests of the soil-structure system model have been presented, which agree well with those obtained from analysis by using the proposed model.     

Two-dimensional translation,rocking, and waves in a building during soil-structure interaction excited by a plane earthquake SV-wave pulse

A two-dimensional (2-D) model of a building supported by a rectangular, flexible foundation embedded in the soil is analyzed for excitation by an incident plane SV-wave. The incidence is below the critical angle. The building is assumed to be anisotropic and linear while the soil and the foundation are assumed to be isotropic and can experience nonlinear deformations. In general the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy and thus less energy is available for the excitation of the building. We show that the energy distribution in the building depends on the nature of the incident wave and differs substantially between the cases of incident P- and SV-waves. However, for both excitation by a plane SV-wave pulse and excitation by a P-wave, we show that the nonlinear response in the soil and the foundation does not significantly change the nature of excitation of the base of the building. It is noted that the building response can be approximated by translation and rocking of the base only for excitation by long, strong motion waves.     

Time-domain boundary element method in viscoelasticity with application to a spherical cavity

The weighted-residual technique, the indirect boundary element method, the truncated indirect boundary element method and the direct boundary element method can be used to analyse nonlinear soil-structure interaction in the time domain. They are illustrated and compared by using the one-dimensional dynamic problem of the spherical cavity in an infinite space. For realistic time steps, all formulations lead to accurate results, but the weighted-residual technique and the truncated indirect boundary element method are much more efficient than the direct boundary element method in the time domain. Hysteretic damping leads to noncausal behaviour, which can, however, be neglected from a practical point of view.     

三维土-结构动力相互作用的一种时域直接分析方法

本文提出了一种分析三维土-结构动力相互作用的时域直接方法。该方法采用集中质量显式有限元和透射人工边界模拟无限域地基,通过编制的FORTRAN程序实现;采用ANSYS软件对上部结构进行建模分析,并通过FORTRAN程序对ANSYS软件的调用,实现了土与结构系统在地震作用下的整体分析。该方法为显隐式相结合的方法,地基和上部结构可采用不同的时间步距进行分析,可大大提高效率。通过两算例,验证了该方法的可行性。     

A lumped mass Chebyshev spectral element method and its application to structural dynamic problems

A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems, as the computational efforts can be greatly reduced in the process of mass matrix inversion. In this study, the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method (CSEM). A Gauss-Lobatto type quadrature, based on Gauss-Lobatto-Chebyshev points with a weighting function of unity, is thus derived. With the aid of this quadrature, the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems. Several types of lumped mass Chebyshev spectral elements are designed, including rod, beam and plate elements. The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation, accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method (FEM). Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart, and is more accurate than classical FEM. For the simulation of elastic wave propagation in structures induced by high-frequency loading, this method achieves satisfactory performance in accuracy and efficiency.

     

Contact stresses and ground motion generated by soil-structure interaction

A study has been made of the dynamic contact stresses that the foundation of a nine-storey reinforced concrete building exerts on the soil during forced vibration tests. The effects of the flexibility of the foundation on the contact stress distribution and on the force-displacement relationship for the foundation have been examined in an attempt at testing several simplifying assumptions commonly used in soil-structure interaction studies. Comparisons of calculated and observed ground displacements induced by soil-structure interaction in the immediate neighbourhood of the building have also been presented.     

基于子结构方法的土-结构动力相互作用半解析方法研究现状综述

寻求高效实用的力学模型和计算方法是土与基础动力相互作用效应在工程设计中得以考虑的关键。围绕3个问题对可以通过手算或自主编程解决土-基础-结构系统动力相互作用问题的半解析子结构法展开评述:（1）为何采用子结构法研究土与结构动力相互作用问题;（2）如何求解子结构法中作为关键参数的基础振动阻抗;（3）如何利用振动阻抗求解上部结构的动力响应。最后,结合实际工程问题探讨了在已有成果的基础上可进行深化和拓展的研究方向。     

The discrete wave number formulation of boundary integral equations and boundary element methods: A review with applications to the simulation of seismic wave propagation in complex geological structures

We review the application of the discrete wave number method to problems of scattering of seismic waves formulated in terms of boundary integral equation and boundary element methods. The approach is based on the representation of the diffracting surfaces and interfaces of the medium by surface distributions of sources or by boundary source elements, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green's functions are evaluated by the discrete wave number method, and the boundary conditions yield a linear system of equations. The inversion of this system allows the calculation of the full wave field in the medium. We investigate the accuracy of the method and we present applications to the simulation of surface seismic surveys, to the diffraction of elastic waves by fractures, to regional crustal wave propagation and to topographic scattering.     

基于ABAQUS的粘弹性边界单元及在重力坝抗震分析中的应用

考虑了2种不同的地震输入模型,即无质量地基模型和考虑辐射阻尼的粘弹性边界模型。以大型非线性有限元程序ABAQUS为平台,采用FORTRAN语言开发了用户单元子程序VSB_UEL.for,将粘弹性边界有效地嵌入到ABAQUS中。在尽量避免求解自由场的前提下,将离散的地震荷载转化为等效结点荷载,编写的计算程序可以方便地将等效荷载施加到人工边界结点上,并通过数值算例验证了粘弹性边界单元及波动输入程序的正确性,其求解效率和计算精度均令人满意,最后将该程序应用到在建的某水电站厂房坝段的抗震分析中。结果表明,与传统的固定边界无质量地基相比,考虑了粘弹性人工边界后,坝体的动力响应峰值减小了20%~40%;在进行结构动力响应分析时,考虑无限域地基的辐射阻尼影响是很有必要的。文中的用户子程序及波动输入程序很容易扩展至三维,为同类工程的抗震分析提供了简洁、合理的计算模式。     

A hybrid analysis method for linear dynamic soil-structure interaction in time and frequency domain

IntroductionThe analysis of dynamic soil-structure interaction for important engineering project is still based on linear model (including equivalent linear model) with complex damping, and traditional frequency domain method (Lysmer, et al, 1975, 1981; DING, et al, 1999). Namely, first calculating frequency domain solution by Fourier transform, and then calculating time domain solution by Fourier inverse transform. The motion equation of a system in frequency domain is usually written as (…     

Site effects and soil-structure interaction in the valley of Mexico

An engineering approach is proposed for representing both site effects and soil-structure interaction in extended alluvial valleys, by using the one-dimensional model of shear were propagation corrected empirically to account for lateral heterogeneities and generated surface waves. The peak structural response is expressed by means of spectral contours that are a function of the predominant period of the site and the fundamental period of the structure. Variations of the peak spectral ordinates with the prevailing site period can be deduced from these contours. A number of events of firm ground, representative of the most dangerous earthquakes expected in Mexico City, are assumed as design earthquakes. Making use of the resulting spectral contours, the provisions for site effects recommended in the Mexican seismic code are evaluated. Also, considering as control motion the 1985 Michoacan earthquake recorded at a representative firm site, spectral contours with soil-structure interaction are obtained which allow one to identify the significant interaction effects originating in the Valley of Mexico for medium- and long-period structures. The influence and relative importance of the critical parameters involved are examined within practical ranges of interest.