Three-dimensional dynamic soil–structure interaction analysis in the time domain

A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil–structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the effects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite-element method, is used and the structure is modelled by 8–21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary finite-element method resulting in significant reduction in computational effort with little loss of accuracy. The approximations also lead to a very efficient scheme for evaluation of convolution integrals in the calculation of soil–structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil–Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil–structure interaction as well as in the analysis of wave scattering and diffraction by three-dimensional surface irregularities. The scattering and diffraction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very efficient for problems which involve low frequencies of interest for earthquake engineering. Copyright © 1999 John Wiley & Sons Ltd     

Seismic soil–structure interaction in multi‐span bridges: Application to a railway bridge

The effects of soil‐structure interaction on the seismic response of multi‐span bridges are investigated by means of a modelling strategy based on the domain decomposition technique. First, the analysis methodology is presented: kinematic interaction analysis is performed in the frequency domain by means of a procedure accounting for radiation damping, soil–pile and pile‐to‐pile interaction; the seismic response of the superstructure is evaluated in the time domain by means of user‐friendly finite element programs introducing suitable lumped parameter models take into account the frequency‐dependent impedances of the soil–foundation system. Second, a real multi‐span railway bridge longitudinally restrained at one abutment is analyzed. The input motion is represented by two sets of real accelerograms: one consistent with the Italian seismic code and the other constituted by five records characterized by different frequency contents. The seismic response of the compliant‐base model is compared with that obtained from a fixed‐base model. Pile stress resultants due to kinematic and inertial interactions are also evaluated. The application demonstrates the importance of performing a comprehensive analysis of the soil–foundation–structure system in the design process, in order to capture the effects of soil‐structure interaction in each structural element that may be beneficial or detrimental. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic soil–structure interaction of massive flexible strip-foundations embedded in layered soils by hybrid BEM–FEM

A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response.     

A comparison of time-domain transmitting boundaries

A non-linear interaction analysis with a (generalized) non-linear structure and a linear unbounded soil is analysed in the time domain, based either on the sub-structure method, which involves global convolution integrals, or on the direct method with local boundary conditions. Alternatively, the hybrid frequency–time-domain method of analysis, which is an iterative scheme, could be used. Approximate local boundary conditions to model the wave propagation towards infinity on the artificial boundary used in the direct method of non-linear soil–structure-interaction analysis to be performed in the time domain are examined. A semi-infinite rod supported elastically, which exhibits the same properties as certain unbounded soils such as dispersion and a cut-off frequency, is used for the investigation. For a transient excitation, the superposition boundary with frequent averaging, the well-known viscous damper and the extrapolation algorithm lead to good accuracy. Moving the artificial boundary further away from the structure (or more precisely, increasing the ratio of the distance of the artificial boundary to the wave length) improves the accuracy.     

A seismic free field input model for FE-SBFE coupling in time domain

A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element (SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space. To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built on unbounded soil. Supproted by: the National Key Basic Research and Development Program under Grant No. 2002CB412709     

Dynamic behaviour of turbine-generator-foundation systems

In this paper a comprehensive investigation on the dynamic characteristics of turbine–generator–foundation systems is performed. All the major components of the system, including turbine–generator casing, shaft, rotors, journal bearings, deck, piers, foundation mat, piles, and soil medium, have been included. Full interaction between the turbine–generator set, the foundation superstructure, and the soil medium, is considered. A hybrid method is used to establish the mathematical model for the turbine–generator-foundation system. The analysis is conducted in the frequency domain through complex frequency response analysis. The response in the time domain is obtained by Fourier transform. The seismic excitation is represented as the control motion on the ground surface, which is generated as an artificial earthquake. A 300 MW turbine-generator-foundation system is analysed under excitations from rotor unbalances and earthquakes. The influence of turbine-generator casing and soil anisotropy on the response of the system is explored. It is found that the presence of casing and soil anisotropy strongly influences the displacements and internal forces of the system under rotor unbalance excitation. Under seismic excitation, however, although the presence of casing and soil anisotropy does affect the displacements of the system, their effect on the internal forces of the system is minimal.     

三维土-结构动力相互作用体系分析的两步时域显式波动有限元过程

为减少直接分析三维大尺度复杂土-结构动力相互作用问题的计算量,提高计算效率,本文直接从波动方程出发,提出了较常规子结构法更简单的两步简化计算过程,即第一步简化上部复杂结构体系为集中质量杆系模型,并求基础处等效输入,第二步通过等效输入求上部结构各位置的动力反应.其中第一步计算主要采用集中质量显式有限单元法结合局部透射人工...     

Response of unbounded soil in scaled boundary finite‐element method

The scaled boundary finite‐element method is a powerful semi‐analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure–soil interface. This permits the analysis of dynamic soil–structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three‐dimensional vector‐wave equation of elasto‐dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high‐frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first‐order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure–soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half‐space with the results of the boundary‐element method is observed. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical modelling of wave propagation in anisotropic soil using a displacement unit-impulse-response-based formulation of the scaled boundary finite element method

An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to soil–structure interaction problems involving scalar and vector waves, unbounded domains of arbitrary geometry and anisotropic soil. The scaled boundary finite element method is employed to derive a novel equation for the displacement unit-impulse response matrix on the soil–structure interface. The proposed method is based on a piecewise linear approximation of the first derivative of the displacement unit-impulse response matrix and on the introduction of an extrapolation parameter in order to improve the numerical stability. In combination, these two ideas allow for the choice of significantly larger time steps compared to conventional methods, and thus lead to increased efficiency. As the displacement unit-impulse response approaches zero, the convolution integral representing the force–displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. Numerical examples demonstrate the accuracy and high efficiency of the new method for two-dimensional soil–structure interaction problems.     

Time domain procedure of FE-BE-IBE coupling for seismic interaction of arch dams and canyons

A procedure for three-dimensional (3-D) coupling of finite elements (FEs), boundary elements (BEs) and infinite boundary elements (IBEs) is presented for the numerical modelling of seismic interaction between arch dams and rock canyons. First, a system of coupling 3-D boundary and infinite boundary elements is developed for simulation of infinite and irregular canyons and for determination, in the frequency domain, of impedance functions on the dam-canyon interface. Secondly, the impedance functions for all degrees-of-freedom are transformed approximately into frequency independent discrete parameters by a curve fitting technique. Finally, these discrete parameters are combined with the dam structure which is discretized by finite elements, thus allowing the response of the arch dam-canyon system to be evaluated. The proposed procedure is efficient because it permits the seismic analysis of arch dam-canyon interaction by the substructure technique in the time domain. To demonstrate both the validity and efficiency of the present procedure, the response of an arch dam-canyon system is obtained under unit impulse acting on the dam-canyon interface as the free field input. Very good agreement is noted when comparing the frequency response determined from the time domain with that from the frequency domain under harmonic excitation applied on the interface of the dam-canyon.     

Efficient seismic analysis for nonlinear soil-structure interaction with a thick soil layer

The direct finite element method is a type commonly used for nonlinear seismic soil-structure interaction(SSI) analysis. This method introduces a truncated boundary referred to as an artificial boundary meant to divide the soilstructure system into finite and infinite domains. An artificial boundary condition is used on a truncated boundary to achieve seismic input and simulate the wave radiation effect of infinite domain. When the soil layer is particularly thick, especially for a three-dimensional problem, the computational efficiency of seismic SSI analysis is very low due to the large size of the finite element model, which contains an whole thick soil layer. In this paper, an accurate and efficient scheme is developed to solve the nonlinear seismic SSI problem regarding thick soil layers. The process consists of nonlinear site response and SSI analysis. The nonlinear site response analysis is still performed for the whole thick soil layer. The artificial boundary at the bottom of the SSI analysis model is subsequently relocated upward from the bottom of the soil layer(bedrock surface) to the location nearest to the structure as possible. Finally, three types of typical sites and underground structures are adopted with seismic SSI analysis to evaluate the accuracy and efficiency of the proposed efficient analysis scheme.     

Seismic isolation for low‐to‐medium‐rise buildings using granulated rubber–soil mixtures: numerical study

This paper presents the preliminary research works on a potential seismic isolation method that makes use of scrap rubber tires for the protection of low‐to‐medium‐rise buildings. The method involves mixing shredded rubber tire particles with soil materials and placing the mixtures around building foundations, which provides a function similar to that of a cushion. Meanwhile, the stockpiling of scrap tires is a significant threat to our environment, and the engineering community has been looking for long‐term viable solutions to the recycling and reuse of rubber. A finite element program has been developed for modeling the time‐domain dynamic responses of soil–foundation–structure system, by which the effectiveness and robustness of the proposed method have been evaluated. In general, the structural responses, in terms of acceleration and inter‐story drift, can be reduced by 40–60%. Copyright © 2012 John Wiley & Sons, Ltd.     

Soil–pile–structure interaction under SH wave excitation

A continuum model for the interaction analysis of a fully coupled soil–pile–structure system under seismic excitation is presented in this paper. Only horizontal shaking induced by harmonic SH waves is considered so that the soil–pile–structure system is under anti‐plane deformation. The soil mass, pile and superstructure were all considered as elastic with hysteretic damping, while geometrically both pile and structures were simplified as a beam model. Buildings of various heights in Hong Kong designed to resist wind load were analysed using the present model. It was discovered that the acceleration of the piled‐structures at ground level can, in general, be larger than that of a free‐field shaking of the soil site, depending on the excitation frequency. For typical piled‐structures in Hong Kong, the amplification factor of shaking at the ground level does not show simple trends with the number of storeys of the superstructure, the thickness and the stiffness of soil, and the stiffness of the superstructure if number of storeys is fixed. The effect of pile stiffness on the amplification factor of shaking is, however, insignificant. Thus, simply increasing the pile size or the superstructure stiffness does not necessarily improve the seismic resistance of the soil–pile–structure system; on the contrary, it may lead to excessive amplification of shaking for the whole system. Copyright © 2003 John Wiley & Sons, Ltd.     

Three-dimensional nonlinear analysis for seismic soil–pile-structure interaction

A three-dimensional method of analysis is presented for the seismic response of structures constructed on pile foundations. An analysis is formulated in the time domain and the effects of material nonlinearity of soil on the seismic response are investigated. A subsystem model consisting of a structure subsystem and a pile-foundation subsystem is used. Seismic response of the system is found using a successive-coupling incremental solution scheme. Both subsystems are assumed to be coupled at each time step. Material nonlinearity is accounted for by incorporating an advanced plasticity-based soil model, HiSS, in the finite element formulation. Both single piles and pile groups are considered and the effects of kinematic and inertial interaction on seismic response are investigated while considering harmonic and transient excitations. It is seen that nonlinearity significantly affects seismic response of pile foundations as well as that of structures. Effects of nonlinearity on response are dependent on the frequency of excitation with nonlinearity causing an increase in response at low frequencies of excitation.     

多点激励下拱桥竖向地震反应的简化计算方法

以某大跨公路拱桥为例,通过对拱桥在三种行波输入模式下地震反应的对比计算,提出了拱脚行波输入的简化输入方式;利用拱桥结构的对称性特点,提出了多点输入下半拱叠加的简化计算方法。经验证,这一计算方法具有良好的计算精度,可将较为复杂的拱桥多点输入地震反应计算问题,转化为工程技术人员熟悉的一致输入下地震反应计算问题。     

分析土和结构相互作用的一种实用耦合方法

提出一种新的数值解与解析解耦合的理论和计算方法,研究土-结构相互作用(SSI)体系的地震动力响应。采用大型有限元软件OpenSees模拟复杂结构的非线性行为,用等效线弹性频域内解析解模拟地基土的行为,使用时域离散递归方法将频域内的解析解转化到时域内,再通过子结构边界上力和位移的协调条件来求解。二者之间的耦合和实时数据交流通过CS集成方法来实现。以一个单自由度算例和一个实际工程为例,验证此方法的精度、稳定性和工程实用性,对比在考虑和不考虑SSI体系情况下结构动力响应的区别。本文所提的耦合SSI计算方法和部分研究成果可为工程设计人员提供参考。     

Free‐vibration analysis of a three‐dimensional soil–structure system

A procedure which involves a non‐linear eigenvalue problem and is based on the substructure method is proposed for the free‐vibration analysis of a soil–structure system. In this procedure, the structure is modelled by the standard finite element method, while the unbounded soil is modelled by the scaled boundary finite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam–foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also verified by the Fourier transform of the impulsive response calculated in the time domain by the three‐dimensional soil–structure–wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are significantly different due to the different definition of damping ratio. This study shows that although the classical mode‐superposition method is not applicable to a soil–structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil–structure system. Copyright © 2001 John Wiley & Sons, Ltd.     

SOIL–PILE–BRIDGE SEISMIC INTERACTION: KINEMATIC AND INERTIAL EFFECTS. PART I: SOFT SOIL

A substructuring method has been implemented for the seismic analysis of bridge piers founded on vertical piles and pile groups in multi-layered soil. The method reproduces semi-analytically both the kinematic and inertial soil–structure interaction, in a simple realistic way. Vertical S-wave propagation and the pile-to-pile interplay are treated with sufficient rigor, within the realm of equivalent-linear soil behaviour, while a variety of support conditions of the bridge deck on the pier can be studied with the method. Analyses are performed in both frequency and time domains, with the excitation specified at the surface of the outcropping (‘elastic’) rock. A parameter study explores the role of soil–structure interaction by elucidating, for typical bridge piers founded on soft soil, the key phenomena and parameters associated with the interplay between seismic excitation, soil profile, pile–foundation, and superstructure. Results illustrate the potential errors from ignoring: (i) the radiation damping generated from the oscillating piles, and (ii) the rotational component of motion at the head of the single pile or the pile-group cap. Results are obtained for accelerations of bridge deck and foundation points, as well as for bending moments along the piles. © 1997 by John Wiley & Sons, Ltd.     

A frequency‐dependent and intensity‐dependent macroelement for reduced order seismic analysis of soil‐structure interacting systems

The computational demand of the soil‐structure interaction analysis for the design and assessment of structures, as well as for the evaluation of their life‐cycle cost and risk exposure, has led the civil engineering community to the development of a variety of methods toward the model order reduction of the coupled soil‐structure dynamic system in earthquake regions. Different approaches have been proposed in the past as computationally efficient alternatives to the conventional finite element model simulation of the complete soil‐structure domain, such as the nonlinear lumped spring, the macroelement method, and the substructure partition method. Yet no approach was capable of capturing simultaneously the frequency‐dependent dynamic properties along with the nonlinear behavior of the condensed segment of the overall soil‐structure system under strong earthquake ground motion, thus generating an imbalance between the modeling refinement achieved for the soil and the structure. To this end, a dual frequency‐dependent and intensity‐dependent expansion of the lumped parameter modeling method is proposed in the current paper, materialized through a multiobjective algorithm, capable of closely approximating the behavior of the nonlinear dynamic system of the condensed segment. This is essentially the extension of an established methodology, also developed by the authors, in the inelastic domain. The efficiency of the proposed methodology is validated for the case of a bridge foundation system, wherein the seismic response is comparatively assessed for both the proposed method and the detailed finite element model. The above expansion is deemed a computationally efficient and reliable method for simultaneously considering the frequency and amplitude dependence of soil‐foundation systems in the framework of nonlinear seismic analysis of soil‐structure interaction systems.