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.     

Dynamic impedances of pile groups with embedded caps in homogeneous elastic soils using CIFECM

Significant research has been reported on the dynamic analysis of pile groups. However, in most of the cases, the effect of pile cap is neglected despite the fact that there may be additional interactions due to the presence of the cap. This paper presents the dynamic impedances for the pile groups with caps embedded in isotropic homogeneous elastic soils. A general three-dimensional finite element procedure is developed. The system is sub-structured into bounded near-field and an unbounded far-field. The pile-soil system of the near-field is modeled using solid finite elements, and the unbounded elastic soil system of the far-field is modeled using the consistent infinitesimal finite element cell method (CIFECM) in the frequency domain.     

Soil-structure interaction using BEM–FEM coupling through ANSYS software package

The main aim of this work is to develop, verify and apply in simulation study an efficient hybrid approach to study seismic response of a soil-structure system taking into account all the important components as: (1) the line time-harmonic source with its specific geophysical properties; (2) the inhomogeneity and heterogeneity of the wave path from the source to the local geological region; (3) the geotechnical properties of the near-field local geological profile and finally (4) the properties of the engineering structure itself. Plane strain state is considered. The hybrid computational tool is based on the boundary element method (BEM¹) for modeling the infinite far-field geological media and finite element method (FEM²) for treating the dynamic behavior of the structure and the near-field finite soil geological region. Each of the two techniques is applied in that part of the whole model where it works more efficiently. The hybrid numerical scheme is realized via the sub-structure approach, direct BEM¹, conventional FEM² and insertion of the BEM¹ model of the seismically active far-field geological media as a macro-finite element (MFE³) in the FEM² commercial program ANSYS. The accuracy and verification study of the proposed method is presented by solution of numerical test examples simulating different seismic scenarios. The obtained results show clearly that the hybrid model is able to demonstrate the sensitivity of the synthetic signals to the source properties, to the heterogeneous character of the wave path, to the relief peculiarities of the local layered geological deposit and to the specific properties of the engineering structure.     

Identification of the Hualien soil-structure interaction system

This article demonstrates how system identification techniques can be successfully applied to a soil-structure interaction system in conjunction with the results of the forced vibration tests on the Hualien large-scale seismic test structure which was recently built in Taiwan for an international joint research. The parameters identified are the shear moduli of several near-field soil regions as well as Young's moduli of the shell sections of the structure. The soil-structure interaction system is represented by the finite element method combined with infinite element formulation for the unbounded layered soil medium. Preliminary investigations are carried out on the results of the static stress analysis for the soil medium and the results of the in-situ tests to divide the soil-structure system into several regions with homogeneous properties and to determine the lower and upper bounds of the parameters for the purpose of identification. Then two sets of parameters are identified for two principal directions based on the forced vibration test data by minimizing the estimation error using the constrained steepest descent method. The simulated responses for the forced vibration tests using the identified parameters show excellent agreement with the test data. The present estimated parameters are also found to be well compared with the average value of those by other researchers in the joint project.     

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 (…     

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。     

Simplified subgrade model for three-dimensional soil-foundation interaction analysis

A simple mechanical model is presented for the three-dimensional dynamic soil-structure interaction analysis of surface foundations. The model is made of one-dimensional vertical beams with distributed mass and horizontal springs which interconnect the two adjacent beams. Its parameters are rather uniquely related with the soil properties alone and thus are minimally dependent on the loading condition and the foundation conditions like geometry, flexibility and size. Formulations are provided to determine the model parameters from the soil properties. Solving the governing equations of this model, expressions for the subgrade behavior in response to the applied load and soil-foundation interaction are developed in analytical forms for various cases. The dynamic and static response of three-dimensional surface foundations are computed by these expressions. It is verified that the model is well capable of reproducing the three-dimensional soil-structure interaction behavior.     

考虑土-结构相互作用双层柱面网壳在多点输入下的地震反应分析

目前对于网壳结构的地震反应研究大部分仍然采用一致输入,特别是没有考虑土-结构相互作用对网壳结构的影响。本文通过对大型有限元分析软件MSC.Nastran的二次开发,用等效线性化方法考虑土体的非线性,对土体采用三维实体单元建模,并对土体在基岩面上采用地震动的多点输入,计算分析了大跨度双层柱面网壳的动力反应,并且与一致地震动输入下网壳结构的地震反应进行了对比,考察了两者之间的差异,深入分析了考虑土-结构相互作用下,双层柱面网壳结构在多点输入和一致输入下的地震反应规律,并得出了一些重要结论。     

Hybrid modelling of a single-layer half-space system in SOIL–structure interaction

A hybrid model is applied to two-dimensional soil–structure interaction problems for the case of a single layer on a halfspace. A continuous impedance function along a semi-cylindrical interface separating the near and far fields is proposed to simulate the radiation of energy and the energy reflection due to the layer of soil. This function as determined by system identification, together with a near-field finite element system, provides a solution for the dynamic analysis of any type of structure.     

动力相互作用分析中无质量地基的应用研究

关于结构-地基的动力相互作用分析已经提出了很多方法，但由于方法复杂而没有得到广泛应用，无质量地基模型仍然是应用最为广泛的近似方法。本文通过结构-地基的动力相互作用分析公式的推导，详细阐明了考虑无限地基影响的动力相互作用分析中无质量地基的概念和应用范围，并通过算例进行了说明。     

Non-linear rocking response of model containment structures

Small (1/24- to 1/8-size) nuclear containment structures were subjected to ground shaking from buried explosions and to oscillating forces. The apparent natural frequency or resonant frequency of rocking varies inversely with amplitude of the shaking. The present paper describes an explicit finite difference model of soil-structure interaction induced by explosive loading. The results indicate that non-linear rocking response is primarily a result of debonding-rebonding and compaction of soil at the soil-structure interface. Measurements of dynamic interface stress and post-test inspection of the interface region tend to confirm these findings.     

On the effective seismic input for non-linear soil-structure interaction systems

Two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately. The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free-field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil-structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil-structure interface of the complete system. It is shown, further, that the free-field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free-field ground motion at a site is usually specified at a single reference point.     

考虑土-结构相互作用的西安钟楼地震反应分析

为探讨土-结构相互作用对西安钟楼地震反应的影响,建立了钟楼上部木结构-台基-地基三维有限元模型,基于粘-弹性人工边界条件,利用振型分解反应谱法进行了地震反应分析。结果表明,考虑相互作用木结构2层相对位移反应增大了2.12倍,台基相对于地面间的相对位移增大了44%。因此,在对钟楼结构进行地震反应分析时必须考虑土-结构相互作用。     

On the seismic performance of straight integral abutment bridges: From advanced numerical modelling to a practice-oriented analysis method

The seismic performance of integral abutment bridges (IABs) is affected by the interaction with the surrounding soil, and specifically by the development of interaction forces in the embankment-abutment and soil-piles systems. In principle, these effects could be evaluated by means of highly demanding numerical computations that, however, can be carried out only for detailed studies of specific cases. By contrast, a low-demanding analysis method is needed for a design-oriented assessment of the longitudinal seismic performance of IABs. To this purpose, the present paper describes a design technique in which the frequency- and amplitude-dependency of the soil-structure interaction is modelled in a simplified manner. Specifically, the method consists of a time-domain analysis of a simplified soil-bridge model, in which soil-structure interaction is simulated by means of distributed nonlinear springs connecting a free-field ground response analysis model to the structural system. The results of this simplified method are validated against the results of advanced numerical analyses, considering different seismic scenarios. In its present state of development, the proposed simplified nonlinear model can be used for an efficient evaluation of the longitudinal response of straight IABs and can constitute a starting point for a prospective generalisation to three-dimensional response.     

Effects of soil-structure interaction on seismic response of PC cable-stayed bridge

This paper attempts to assess the effects of dynamic soil-structure interaction (SSI) on the seismic behavior of a PC cable-stayed bridge placed on a moderately deep soil stratum overlying rigid bedrock, and to evaluate the applicability of a simple mass-spring model in evaluating SSI. Parametric analysis is performed to investigate the significance of SSI under various stiffness, foundation depth conditions using finite element methods. The applicability of a mass-spring model is discussed by comparison with FEM. The results of analysis reveal the influence of SSI on the seismic behavior of bridge-soil system, and recommendations for aseismic design are provided. The mass-spring model proves to be promising for representing the seismic behavior of the bridge-soil system, and the mechanism is interpreted in detail.     

土-结构相互作用分析中几类地震输入方式的比较

地震作用下土-结构动力相互作用的整体有限元分析需要在人工边界处输入地震动。目前可能采用的地震输入方法包括黏弹性边界自由场输入方法、自由场应力方法、自由场位移方法以及侧边界自由方法。由于采用近似人工边界条件或者未完全考虑地震自由场,上述地震输入方法均为近似方法。本文以大开地铁车站二维有限元分析为例,根据规范建议的边界位置,研究了上述地震输入方法的精度,研究成果可为土-结构相互作用分析的合理地震输入提供一定参考。     

3D viscous-spring artificial boundary in time domain

After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems.     

Soil-structure interaction with Rayleigh waves

Presented is a plane-strain method for soil-structure interaction analysis consisting of the superposition of the free field motions and the interaction motions in a generalized seismic environment. The free field is modelled as a horizontally layered viscoelastic medium and the seismic environment may consist of a combination of S, P and Rayleigh waves. The soil-structure system is modelled with viscoelastic finite elements, transmitting boundaries, viscous boundaries and a three-dimensional simulation. Comparative analyses of the same structure are conducted for an input of R waves and for vertically propagating S and P waves in a rock site and sand site. In the rock site the R waves produce higher peak horizontal spectral acceleration up to 25 per cent, and a significant rocking effect at points away from the centre of gravity of the structure. However, the S and P waves show higher peak vertical spectral acceleration by up to 15 per cent at the centre of the structure. Very similar horizontal response, but higher vertical response only at the centre of the structure for S and P waves, is obtained for the sand site.     

An efficient time-domain soil-structure interaction analysis based on the dynamic stiffness of an unbounded soil

An approximate method and a rigorous method are presented for the time-domain soil-structure interaction analysis, both of which use the stiffness of soil obtained numerically or experimentally in the limited frequency range. In the aseismic design of a large-scale structure, the approximate and rigorous methods are intended to be used in a preliminary analysis and a detailed study, respectively. Both methods are based on the approximation that the first few terms of the Fourier or Taylor expansions of a frequency-dependent function are used. The difference lies in the number of coefficients of each series, and also in the manner in which the coefficients can be determined. In order to demonstrate the validity of the proposed methods, a soil-structure system, whose soil has a complex profile under the foundation, is analysed. The dynamic stiffness of the soil is calculated by a 3-D hybrid approach that combines the finite element method and the boundary element method. As a result, the present methods are capable of evaluating the complexity of the soil more precisely and efficiently than conventional methods.     

A simple boundary element formulation and its application to wavefield excited soil-structure interaction

A simple boundary element formulation which is based directly on the point load solutions for an elastic full-space is presented. It is integrated in a finite element program to calculate dynamic soil-structure interaction problems. The combined boundary and finite element method is applied to structures which are excited by horizontally propagating waves in the soil. For three different types of flexible structure-elastic beams, low and high (square) shear walls-and the corresponding rigid structures the vibration modes and the soil-structure transfer functions have been investigated. The flexible foundations display the same wave pattern as the exciting free-field of the soil, but the amplitudes are reduced with increasing frequency, depending on the stiffness or wave resistance of the structure. Rigid structures show, in part, quite different behaviour, giving free-field reductions caused by kinematic and inertial soil-structure interaction.