Equivalent fixed-base models for soil-structure interaction systems

To simplify the consideration of the soil-structure interaction (SSI) effects, a single degree-of-freedom (SDOF) replacement oscillator has been successfully utilized to represent an SSI system with SDOF structural model. In the present paper, this approximation is first extended to an equivalent fixed-base model with modified system parameters. Based on this generalization, a methodology is then proposed to determine the equivalent fixed-base models of a general multi degree-of-freedom SSI system using simple system identification techniques in the frequency domain. Various fixed-base models are formulated and their accuracy is compared for a five-story shear building resting on soft soil. It is shown that the actual SSI system can be accurately represented with an appropriate fixed-base model.     

Base-isolated buildings with soil-structure interaction

The equations of motion of building systems with soil-structure interaction are formulated for foundations comprising a joint mat or a set of individual spread footings. The influence of soil-structure interaction and the possible effects of building and foundation rocking are examined by investigating the modal properties. Simplifications in the analysis are also suggested.     

Evaluation of FEMA-440 for including soil-structure interaction

Replacing the entire soil-structure system with a fixed base oscillator to consider the effect of soil-structure interaction (SSI) is a common analysis method in seismic design. This technique has been included in design procedures such as NEHRP, ASCE, etc. by defining an equivalent fundamental period and damping ratio that can modify the response of the structure. However, recent studies indicate that the effects of SSI should be reconsidered when a structure undergoes a nonlinear displacement demand. In recent documents on Nonlinear Static Procedures (NSPs), FEMA-440 (2005), a modified damping ratio of the replacement oscillator was proposed by introducing the ductility of the soil-structure system obtained from pushover analysis. In this paper, the damping defined in FEMA-440 to include the soil-structure interaction effect is evaluated, and the accuracy of the Coefficient Method given in FEMA-440 and the Equivalent Linearization Method is studied. Although the improvements for Nonlinear Static Procedures (NSPs) in FEMA-440 are achieved for a fixed base SDOF structure, the soil effects are not perfectly obtained. Furthermore, the damping definition of a soil-structure system is extended to structures to consider bilinear behavior.     

Efficient modal analysis for structures with soil-structure interaction

An efficient methodology is presented which uses modal analysis implemented in the frequency domain to obtain the structural response of a system with soil-structure interaction. The interaction effects are represented using a free-field ground motion modification factor, derived for each mode of vibration and used in the determination of structural response. Applying this algorithm, the advantages of the modal superposition method are fully exploited, and the interaction problem can be solved easily and effectively within the framework of the conventional frequency domain analysis for a fixed-base structure. In addition, this method produces accurate approximation with less computational effort due to consideration of only the first few vibration modes of the structure.     

考虑土-结构动力相互作用效应的界限研究

开展了土-结构动力相互作用的模型试验,探讨了框架结构的近似有效基本周期,并研究了考虑相互作用效应的界限.模型试验中分别进行了刚性地基和柔性地基条件下的结构基本周期测试,并通过与理论计算结果的比较,验证了FEMA450中建议的有效基本周期计算方法能够有效预测土-结构相互作用效应的影响.利用FEMA450中建议的刚性地基上普通钢筋混凝土框架结构基本周期近似值的计算式,分别建立了明置基础、埋置基础的框架结构有效基本周期近似值的计算式,并以此分析了框架结构考虑相互作用的界限问题,提出了考虑埋置深度影响的合理界限.     

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.     

Seismic wave effects on soil-structure interaction

One of the most common hypotheses implicit in the seismic analyses of structures is that the earthquake input motion is identical at all points beneath the structure. Very little experimental evidence presently is available to supplant this viewpoint. However, one may infer a spatially distributed surface motion of the soil if the earthquake is simply assumed to consist of a complex of surface waves traversing the plan of the structural site. Under these conditions, as shown in the paper, the effects of passing waves must be integrated over the structural area to obtain their net effects as exciting functions to the structure. When this is done for individual Fourier components of the quake, one important result is the diminution or ‘self-cancelling’ effect of some inputs, particularly for those waves the wavelengths of which are comparable to the dimensions of the structure, or shorter. Another important effect is the torsional excitation of the structure. The present paper is not necessarily aimed at replacing present analysis methods but at discussing some of the effects which will inevitably be entrained by the introduction of any information or hypotheses regarding the spatial distribution of earthquake motions. This analysis tends to suggest why higher frequencies are of lesser importance for a structure having a large rigid foundation.     

Three-dimensional hybrid modelling of soil-structure interaction

A three-dimensional hybrid model for the analysis of soil-structure interaction under dynamic conditions is developed which takes advantage of the desirable features of the finite element and substructure methods and which minimizes their undesirable features. The modelling is achieved by partitioning the total soil-structure system into a near-field and a far-field with a hemispherical interface. The near-field, which consists of the structure to be analysed and a finite region of soil around it, is modelled by finite elements. The semi-infinite far-field is modelled by distributed impedance functions at the interface which are determined by system identification methods. Numerical results indicate that the proposed model makes possible realistic and economical assessment of three-dimensional soil-structure interaction for both surface and embedded structures.     

Centrifugal modelling of dynamic soil-structure interaction

This paper presents a centrifuge model that is capable of realistically representing soil-structure systems subjected to earthquake-like excitation. The model is validated by performing (i) free field soil tests, (ii) dynamic soil-structure interaction tests and (iii) a numerical analysis of the experimental results. The free field experiments show that the simulated earthquake, which is generated by the hammer-exciter plate method, is similar in amplitude and frequency content to a real earthquake. The experiments also demonstrate that a confined soil sample can satisfactorily model a horizontal soil stratum of infinite lateral extent when the containment walls are lined with an absorptive material to attenuate wave reflections that would otherwise occur. Measurements of the acceleration at different locations on the free soil surface indicate that the surface motion is fairly uniform over a relatively large area. This is further confirmed by a comparison made between the measured free and scattered field motions for a surface foundation. Next, a series of soil-structure interaction tests are performed which examine the dependence of radiation damping on the natural frequencies of the structure relative to the fundamental frequency of the soil stratum. The experimental results are shown to be consistent with established theories. Finally, the experimental results are used to compute the stiffness and damping parameters of a two degree of freedom numerical model of the soil-structure system. The experimental parameters are shown to be in good agreement with calssical text book formulae. This study demonstrates that the centrifuge model consistently behaves as expected for simple, but realistic, dynamic soil and soil-structure systems, and can, therefore, be used with confidence to examine more complicated systems that are not yet fully understood.     

Implementation of effective seismic input for soil-structure interaction systems

A previously introduced method for transmitting effective seismic excitation to a discretized soil-structure system implemented. The method permits free-field excitation of a linear soil system to be specified within the regie of computation, arbitrarily close to a zone that includes the (possibly non-linear) structure and local subgrade and bae, thus eliminating the need to transmit the seismic excitation through artificial boundaries. This approach is demonse through a numerical example comprising a linear, two-dimensional system. Some comments also are made on the rere efficiencies of various local absorbing boundaries.     

Smoothed response spectra including soil-structure interaction effects

Elastic response spectra that take into account the effects of soil-structure interaction on soft soils are developed. The response spectra are calculated utilizing a 3 DOF system including deformations of the superstructure and foundation. The equations of motion of the system are solved using direct integration under normalized earthquake records. Statistical processing of the results is implemented resulting in response spectra for "short and dense buildings with low interaction", "short and dense buildings with high interaction", "tall and light buildings with low interaction" and "tall and light buildings with high interaction". The resulting response spectra are smoothed and discussed.     

Hybrid experiments on non-linear earthquake-induced soil-structure interaction

Non-linear seismic soil-structure interaction is studied through a hybrid procedure using the pseudo-dynamic testing (PDT) method which is modified to take into account frequency dependence and developed for foundation-soil systems. The numerical scheme used in conventional PDT is improved by introduction of a time-dependent pseudo-forcing function which is derived from frequency-dependent dynamic characteristics of the system by means of Hilbert transformation in the frequency domain. Surface, shallow and caisson foundation models that differed in size and depth of embedment were used. The mechanical characteristics of the systems were determined from static and forced vibration dynamic tests. An amplitude scaling technique was used for three recorded accelerograms.     

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.     

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.     

考虑土-结构动力相互作用的TMD结构减震控制

本文分析了TMD(Tuned mass damper)在刚性地基和柔性地基情况下的减震控制机理,以某6层钢筋混凝土框架结构为研究对象,分别考虑了土-结构动力相互作用对无TMD控制结构的影响,场地条件对TMD减震控制性能的影响和土-结构动力相互作用对TMD减震控制性能的影响。通过分析得出TMD控制系统的减震效果除了与输入地震动特性有关外,还与场地条件、上部结构和基础的动力特性等因素有关。如果土-结构动力相互作用体系的自振周期远离输入地震动的卓越周期,则相互作用体系的地震响应较小。地基土越软,框架建筑结构层间相对位移地震响应也就越小。如果考虑土-结构动力相互作用效应的影响设计TMD调频系统的自振周期,则TMD的控制效果会有一定程度的提高。     

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.     

结构-地基相互作用体系动力特性参数的简化计算方法

本文首先介绍了几种计算结构－地基相互作用体系动力特性的简化方法，并用振动台模型试验的数据资料进行计算分析，讨论了各方法的局限性；在此基础上，提出了一种改进的简化计算方法。在该方法中，主要改进是合理考虑了桩基对体系刚度的贡献。     

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.     

Influence of foundation flexibility on soil-structure interaction

The effect of the base mat flexibility on seismic soil-structure interaction is studied for an axisymmetric reactor building on a soft and a stiff soil. As a preliminary step, the dynamic response of a massless flexible circular plate with two rigid concentric walls, through which the plate is loaded, is analysed. The response of the plate is found to depend on the plate flexibility, the load distribution and the frequency of excitation. For practical, in-phase load distributions, the response of the flexible plate is close to that of a rigid plate at low frequencies, but deviates at high frequencies. Including the flexibility of the mat has hardly any effect on the frequencies and damping of the fundamental rocking and vertical modes of the reactor building. This is the case for soft and stiff soil conditions. However, the flexibility of the mat strongly affects the first and higher structural deformation modes. In both cases the amount of energy dissipated in the soil is a significant percentage of the total dissipation, and is essentially unaffected by the mat flexibility.