Accidental eccentricity in symmetric buildings due to wave passage effects arising from near‐fault pulse‐like ground motions

This article investigates the characteristics of the accidental eccentricity in symmetric buildings due to torsional response arising from wave passage effects in the near‐fault region. The soil–foundation–structure system is modeled as a symmetric cylinder placed on a rigid circular foundation supported on an elastic halfspace and subjected to obliquely incident plane SH waves simulating the action of near‐fault pulse‐like ground motions. The translational response is computed assuming that the superstructure behaves as a shear beam under the action of translational and rocking base excitations, whereas the torsional response is calculated using the mathematical formulation proposed in a previous study. A broad range of properties of the soil–foundation–structure system and ground motion input are considered in the analysis, thus facilitating a detailed parametric investigation of the structural response. It is demonstrated that the normalized accidental eccentricity is most sensitive to the pulse period (T_P) of the near‐fault ground motions and to the uncoupled torsional‐to‐translational fundamental frequency ratio (Ω) of the structure. Furthermore, the normalized accidental eccentricities due to simplified pulse‐like and broadband ground motions in the near‐fault region are computed and compared against each other. The results show that the normalized accidental eccentricity due to the broadband ground motion is well approximated by the simplified pulse for longer period buildings, while it is underestimated for shorter period buildings. For symmetric buildings with values of Ω commonly used in design practice, the normalized accidental eccentricity due to wave passage effects is less than the typical code‐prescribed value of 5%, except for buildings with very large foundation radius. Copyright © 2017 John Wiley & Sons, Ltd.     

Earthquake response analysis of multistorey buildings including foundation interaction

An efficient method, based on the Ritz concept, for dynamic analysis of response of multistorey buildings including foundation interaction to earthquake ground motion is presented. The system considered is a shear building on a rigid circular disc footing attached to the surface of a linearly elastic halfspace. In this method, the structural displacements are transformed to normal modes of vibration of the building on a rigid foundation. The analysis procedure is developed and numerical results are presented to demonstrate that excellent results can be obtained by considering only the first few modes of vibration. As the number of unknowns are reduced by transforming to generalized co-ordinates, the method presented is much more efficient than direct methods.     

Frequency-independent impedances of soil-structure systems in horizontal and rocking modes

The frequency-independent foundation impedances, commonly used in soil-structure dynamic interaction problems, are developed for a circular footing resting on a homogeneous halfspace. As they ignore the structure attached to the foundation, the error introduced in the structural response may be 50 per cent or more in the neighbourhood of the fundamental frequency of the soil-structure system. The present study proposes a new method developed for most dynamic soil-structure interaction problems. The key idea is to retain for the frequency-independent impedances values computed for the fundamental frequency of the soil-structure system; thus these values include the dynamic characteristics of the whole soil-structure system and lead to a satisfactory approximation of the exact solution over a wide frequency range. The method is developed here for the horizontal and rocking modes of a structure with a circular base resting on a homogeneous halfspace. Numerical applications are given for a simple linear oscillator in order to make possible a thorough parametric study. The response of some idealized building-foundation systems to harmonic excitation or to a seismic input is next examined in order to illustrate the efficiency of the proposed model.     

Dynamic response of buildings due to trains in underground tunnels

The interaction of a tunnel-soil-building system due to trains is investigated by a substructure technnique. The soil medium is assumed to be a viscoelastic halfspace. The method of wave function expansion is used to construct the displacement fields in terms of potentials. The total soil-structure interaction problem is decomposed into a foundation radiation problem and a tunnel radiation problem. The impedance matrices for the corresponding substructure problems are obtained using a collocation technique. The steady state response of buildings for a given tunnel-foundation geometry is determined using the impedance matrix. Hence, the response of the building to train loading at different speeds is evaluated and compared with allowable vibration limits.     

Dynamic behaviour of building-foundation systems

A discussion of the effects of soil-structure interaction on the dynamic response of linear structures which respond as single-degree-of-freedom systems in their fixed-base condition is presented. The structures are presumed to be supported at the surface of a homogeneous, elastic halfspace and to be excited at the base. The free-field ground motions investigated include a harmonic motion, a relatively simple pulse-type excitation and an actual earthquake record. Comprehensive response spectra are presented for a range of the parameters defining the problem, and the results are used to assess the accuracy of a simple, approximate method of analysis in which the system is represented by a viscously damped, simple oscillator. Special attention is given to defining the conditions under which the interaction effect is of sufficient importance to warrant consideration in design. The method of analysis used to obtain the numerical data reported herein is reviewed only briefly, the emphasis of the paper being on the interpretation of the results.     

Kinematic soil–structure interaction for long-span cable-supported bridges

A general procedure is presented to study the dynamic soil–structure interaction effects on the response of long-span suspension and cable-stayed bridges subjected to spatially varying ground motion at the supporting foundations. The foundation system is represented by multiple embedded cassion foundations and the frequency-dependent impedance matrix for the multiple foundations system takes into account also the cross-interaction among adjacent foundations through the soil. To illustrate the potential implementation of the analysis, a numerical example is presented in which the dynamic response of the Vincent–Thomas suspension bridge (Los Angeles, CA) subjected to the 1987 Whittier earthquake is investigated. Although both kinematic and inertial effects are included in the general procedure, only the kinematic effects of the soil–structure interaction are considered in the analysis of the test case. The results show the importance of the kinematic soil–foundation interaction on the structural response. These effects are related to the type, i.e. SH-, SV-, P- or Rayleigh waves and to the inclination of the seismic wave excitation. Moreover, rocking components of the foundation motion are emphasized by the embedment of the foundation system and greatly alter the structural response.     

Dynamic response of vertically excited liquid storage tanks considering liquid-soil interaction

The paper presents a dynamic response analysis of vertically excited liquid storage tanks including both liquid-tank and liquid-soil interaction. The system considered is a thin-walled, elastic cylindrical shell entirely filled with an incompressible and inviscid fluid, resting on a flexible foundation over an elastic halfspace with frequency dependent stiffness and damping parameters. The problem is treated analytically by the generalized-coordinate approach and then solved numerically using the complex frequency response analysis. For one special tank, natural frequencies and equivalent damping ratios are evaluated and compared with those corresponding to a rigid ground. The maximum dynamic pressure is calculated using the response spectra of the 1976 Friuli earthquake. A parameter study is carried out to show the great influence of variable soil stiffness upon the damping ratio of the shell-liquid-soil system.     

Vibration of viscoelastic foundations

Simple approximate solutions are presented for the steady-state response of a massless, rigid disk, which is supported at the surface of a linear viscoelastic halfspace and is excited by a harmonically varying horizontal or vertical force, or by a harmonically varying moment about an axis in the plane of the disk. The halfspace is idealized either as a standard Voigt solid or as a constant hysteretic solid. The solution for the massless disk is then applied to the analysis of foundations with mass, and for each mode of excitation, comprehensive numerical data are presented to illustrate the effects of viscoelastic action on the response of both the massless disk and of foundations with mass It is shown that the principal effects of material damping are to increase the damping capacity of the foundation and to reduce its ‘natural’ frequency. In the mathematically equivalent representation of the elastically supported massless disk as a spring-dashpot combination without mass, it is shown that the effective stiffness of the spring may become negative over significant ranges of the exciting frequency, and that it is preferable to model the disk-halfspace system as an oscillator with mass, taking its spring constant equal to the static stiffness of the original system.     

Field verification of a theoretical model to predict the dynamic response of a soft clay deposit

A 40-m thick clay deposit was subjected to sinusoidal excitations using a foundation block and an eccentric mass type vibrator. The response of the foundation block and the surrounding soil was measured using geophones inside the soil and on the surface. The phase shift between the excitation signal and the response signal, the accelerations of the foundation block and the particle velocities in the soil are compared with those obtained from a frequency-dependent numerical model based on the exact analytical solution for the boundary value problem of a rectangular foundation resting on a linear elastic halfspace.     

Soil–structure interaction in the time domain using halfspace Green's functions

A time-domain formulation is proposed for the transient response analysis of general, three-dimensional structures resting on a homogeneous, elastic halfspace subjected to either external loads or seismic motions. The formulation consists of two parts: (a) the time domain formulation of the soil behaviour and (b) the coupling of the corresponding soil algorithms to the Finite Element Code ANSYS. As far as the structure is concerned, this coupling opens the way for the analysis of non-linear soil–structure interaction. The approach is based on halfspace Green's functions for displacements elicited by Heaviside time-dependent surface point loads. Hence, the spatial discretisation can be confined to the contact area between the foundation and the soil, i.e. no auxiliary grid beyond the foundation as for conventional boundary element formulations is required. The method is applied to analyse the dynamic response of a railway track due to a moving wheel set by demonstrating the influence of ‘through-the-soil coupling’.     

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

The non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.     

The effectiveness of trenches in reducing seismic motion

The effect of placing barriers in the travel path of P, SV and SH seismic waves has been studied using time-domain solutions of plane-strain finite element programs for two-dimensional crustal models. The wavefields considered propagate parallel to the free surface of an elastic medium consisting of a single layer over a halfspace. Barriers take the form of open-air trenches. Effects of damping are assessed by considering representative viscoelastic conditions. Computations are presented as the ratio of spectral energy observed at a point with the barrier system in place in the model to the spectral energy observed at the same point without the barrier system in the model. These spectral ratios are dependent upon the direction of wave propagation. The calculations brought to light the marked role of surficial layering and attenuation properties of the surface rocks or soils on the effectiveness of seismic trench barriers. Barrier models without these features cannot in general reliably predict seismic wavefields at the surface. In the range of cases studied, trench depth d rather than width is the most sensitive parameter. When the ratio d/λ, the ratio of trench depth to the wavelength of shear waves, is greater than about 0·6, power spectral ratios of 0·06 and less are found for SH waves and the vertical component of SV motion for frequencies of 4–6 Hz. By contrast, for frequencies less than 3–4 Hz, power spectral ratios from unity to about two and greater are observed, indicating amplification for the horizontal component of wave motion. Spectral ratios calculated at some locations in front of the barrier system show over two-fold amplification. Spectral ratios also change significantly with the relative location of the free surface observation point.     

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.     

Response of pile foundations to rayleigh waves and obliquely incident body waves

The paper presents results of a study on the harmonic response of piles and pile groups embedded in a halfspace to various forms of seismic waves. These include the Rayleigh wave as well as obliquely incident P, SV and SH waves. The pertinent mixed boundary value problems of pile-soil-pile interaction are solved by a numerical model of the boundary integral nature. All modes of foundation vibrations, i.e. translational, rocking and torsional, are included in the model. The results presented are used to highlight the salient features of the seismic response of piles. In addition, the influence of certain pile-soil parameters, such as pile rigidity and pile spacing, on the seismic behaviour of pile foundations is investigated.     

Soil-structure interaction at higher frequency factors

Approximate solutions to the forced vibrations of a rigid circular plate attached to the surface of an elastic halfspace are presented for large values of the frequency factor. These results are important when solving soil-structure interaction problems when such problems involve high-frequency factors. This situation arises when high-frequency components of earthquakes are associated with a relatively rigid foundation of a large base area and located on a soft terrain. Similar situations occur in cases of blast loadings and impact and in the foundations of large high-speed machinery. These solutions are used to solve the problem of the motion of a rigid mass on an elastic halfspace subjected to steady state and transient horizontal accelerations. From these results, it is deduced that a large rigid mat foundation located on soft terrain significantly attenuates input accelerations and consequently may be useful as the foundation of large massive rigid structures such as a nuclear power station.     

Stresses and excess pore pressure induced in saturated poroelastic halfspace by moving line load

This paper examines stresses and excess pore fluid pressure that are induced in a saturated poroelastic soil of halfspace extent by a concentrated line load. The line load is moving at a constant velocity along the surface of the poroelastic halfspace. The governing equations for the proposed analysis are based on the Biot's theory of dynamics in saturated poroelastic soils. The governing partial differential equations are solved using Fourier transforms. The solutions for the stresses and excess pore pressure are expressed in the forms of inverse Fourier transforms. The numerical results are obtained by performing the numerical inversion of the transform integrals. A parametric study is presented to illustrate the influences of the velocity of moving load and the poroelastic material parameters on the stresses and excess pore pressure. At a high velocity, the maximum values of the stresses in a poroelastic halfspace are smaller than those in an elastic solid, whilst at a low velocity the stresses in a poroelastic halfspace are larger than those in an elastic halfspace. The potential of diffusivity has an important influence on the stresses and excess pore pressure.     

Direct finite element method for nonlinear analysis of semi‐unbounded dam–water–foundation rock systems

A direct finite element method is presented for nonlinear earthquake analysis of interacting dam–water–foundation rock systems. The analysis procedure applies viscous damper absorbing boundaries to truncate the semi‐unbounded fluid and foundation‐rock domains and specifies at these boundaries effective earthquake forces determined from the design ground motion defined at a control point on the free surface. The analysis procedure is validated numerically by computing the frequency response functions and transient response of an idealized dam–water–foundation rock system and comparing with results from the substructure method. Because the analysis procedure is applicable to nonlinear systems, it allows for modeling of concrete cracking, as well as sliding and separation at construction joints, lift joints, and at concrete–rock interfaces. Implementation of the procedure is facilitated by commercial finite element software with nonlinear material models that permit modeling of viscous damper boundaries and specification of effective earthquake forces at these boundaries. Copyright © 2017 John Wiley & Sons, Ltd.     

Response of circular flexible foundations subjected to horizontal and rocking motions

A methodology using modal analysis is developed to evaluate dynamic vertical displacements of a circular flexible foundation resting on soil media subjected to horizontal and rocking motions. The influence of the soil reaction forces on the foundation is considered by introducing modal impedance functions, which can be determined by an efficient procedure with ring elements. The displacements of the foundation can then be easily solved by modal superposition. Parametric studies for modal responses of the flexible foundation indicate that the coupled response of the foundation is significantly influenced by relative stiffness among the foundation and the soil medium, vibration frequency range, foundation mass, and boundary contact conditions. The welded boundary condition should be considered to predict the coupling response while the relaxed boundary condition may be used to predict approximately the vertical displacements. As a foundation with a relative stiffness ratio more than three, it is found that the foundation can be considered as rigid to calculate coupling displacements. For a slightly flexible foundation, considerations of three modes are sufficient enough to obtain accurate foundation responses. Moreover, at low frequencies, the coupling effect due to higher mode can be neglected.     

二维地基波阻板隔振分析

本文采用了以薄层法层状半空间基本解答作为格林函数的边界元法,对均质弹性半空间和层状半空间中二维波阻板隔振设计进行了详细的参数分析。分析结果表明,均质弹性半空间和层状半空间内采用波阻板隔振均可取得较好的隔振效果;应保证波阻板具有合理的宽度和较小的埋深,才能得到理想的隔振效果;同时增加波阻板的厚度和模量是提高隔振效果的最有效的2种措施;此外,分层性对波阻板隔振效果也具有一定的影响。     

Earthquake response of structures with partial uplift on winkler foundation

The effects of transient foundation uplift on the earthquake response of flexible structures are investigated. The structural idealization chosen in this study is relatively simple but it incorporates the most important features of foundation uplift. In its fixed base condition the structure itself is idealized as a single-degree-of-freedom system attached to a rigid foundation mat which is flexibly supported. The flexibility and damping of the supporting soil are represented by a Winkler foundation with spring-damper elements distributed over the entire width of the foundation. Based on the response spectra presented for several sets of system parameters, the effects of foundation-mat uplift on the maximum response of structures are identified. The influence of earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects on the response of uplifting structures is also investigated.