Antiplane response of a dike on flexible embedded foundation to incident SH-waves

The response of an elastic circular wedge on a flexible foundation embedded into a half-space is investigated in the frequency domain for incident pane SH-waves. The problem is solved by expansion of the motion in all three media (wedge, foundation and half-space) in cylindrical wave functions (Fourier-Bessel series). The structural model is simple, but accounts for both differential motions of the base and for the effects of soil-structure interaction. Usually, structural models in earthquake engineering consider either differential ground motion, but ignore soil-structure interaction, or consider soil-structure interaction, but for a rigid foundation, thus ignoring differential ground motion. The purpose of the study is to find how stiff the foundation should be relative to the soil so that the rigid foundation assumption in soil-structure interaction models is valid. The shortest wavelength of the incident waves considered in this study is one equal to the width of the base of the wedge. It is concluded that, for this model, a foundation with same mass density as the soil but 50 times larger shear modulus behaves as ‘rigid’. For ratio of shear moduli less than 16, the rigid foundation assumption is not valid. Considering differential motions is important because of additional stresses in structures that are not predicted by fixed-base and rigid foundation models.     

Case study of strong ground motion variations across cut slope

We evaluate the influence of topography on motions recorded at the base and crest of an approximate 3H:1V, 20 m single-faced slope. The motions were recorded during the 1983 Coalinga earthquake mainshock and two aftershocks. Mainshock peak accelerations at the crest and base transverse to the slope face were 0.59 and 0.38 g, respectively. The spectral amplification of crest motion occurred across T≈0–2 s. Differences between the crest/base motions are postulated to result principally from soil-structure interaction (base instrument is in a structure), variations in local ground response, and topography. Transfer functions quantifying soil-structure interaction (SSI) effects are evaluated and the base motion is modified at short periods to correct it to an equivalent free-field motion. The different levels of ground response at the crest and base are identified based on location-specific measurements of soil shear wave velocities. Differences between crest/base motions not accounted for by SSI or differential ground response are attributed to topographic effects. By these means, topographic spectral amplification (i.e. amplification relative to level ground conditions) is estimated to be about 1.2 at the crest and about 0.85–0.9 at the base across the period range T≈0.4–1.0 s.     

土-结构相互作用效应对结构基底地震动影响的试验研究

利用土与结构动力相互作用振动台模型试验数据,通过各种试验工况下土层表面与基础表面加速度反应的比较,深入探讨了土与结构动力相互作用效应对高层建筑结构基底地震动的影响。从输入地震动频谱特性、输入地震动强度水平和上部结构动力特性3个方面详细分析了与SSI效应对高层建筑基底震动影响程度有关的一些因素。结果表明：SSI效应对高层建筑基底地震动的影响与输入地震波的动力特性有很大关系。在地震动的频谱成分方面,SSI效应对高层建筑基底地震动的影响主要体现为土层表面和基础表面在与输入地震动卓越频率相近处的频谱成分有较大差异;SSI效应对高层建筑基底地震动的影响程度随着输入加速度峰值水平的增加而减小;在某一特定地震波作用下,当上部结构的振动频率与地震地面运动的卓越频率相近时,SSI效应对高层建筑基底地震动的影响较为强烈。     

An approximate method for soil-structure interaction for sh-waves—the born approximation

An approximate method is proposed for the scattering of SH-waves by foundations of irregular shape and the resulting soil-structure interaction problems. The scattering of elastic waves by the rigid foundation embedded in half-space is solved approximately by using integral representation of the wave equation. The procedure is the Born approximation which has been widely used in quantum mechanics for collision and scattering theory though not well-known in elastodynamics. This paper extends the previous work of the authors on the scattering of waves to account for soil-structure interaction. The motion of the foundation is evaluated by the balance of momentum under stresses due to the incident waves as well as the waves generated by its own motion and the forces coming from the superstructure. The model investigated consists of an infinitely long elastic shear wall of height H and thickness h erected on a rigid infinitely long foundation. Results are presented for the cases with circular, elliptical and rectangular foundations. For a circular foundation, excellent agreement is found with the exact solutions for the foundation displacement and the relative displacement between the top and bottom of the structure for the entire range of wave numbers. For an elliptical foundation, accuracy decreases with increasing wave numbers. Foundation displacements are compared for foundation shapes that are shallow elliptical, deep elliptical, rectangular and circular. It is observed that foundation displacements are dependent on the angle of incidence except for a semi-circle. The results on the details of the scattered field are, however, not as accurate.     

多层剪切型结构水平地震反应的行波分析

本文根据行波在结构内多次反射并向地基土内散射的概念, 给出了多层剪切型结构水平向地震反应的行波解析解.证明了在考虑土与结构相互作用的情况下, 金井清所导出的根据结构顶部运动推算基底运动的公式仍然成立, 并利用1976年唐山地震时在北京饭店所获得的强震记录, 验证了这一公式.      

Estimating kinematic interaction of raft foundations from earthquake records and its effects on structural response

A practical method for estimating kinematic interaction from earthquake records is presented. The kinematic interaction is characterized by a two-parameter model and these parameters can be estimated by using a frequency-domain systems identification method. The simple model can be used to model both wave passage effects and the effects of incoherent wave fields. Numerical simulation tests show that kinematic interaction parameters can be estimated to their best accuracy by using building base responses and the free-field excitation and can also be estimated by using building responses, base responses and the free-field excitation. The method was applied to two buildings with raft foundations and it was found that kinematic interaction was significant during earthquakes. Published theoretical models (wave passage effect) for vertically incident SH waves can be used to estimate the transfer functions up to 4–5 Hz and the models for horizontally propagating waves under-predict the estimated transfer functions by a significant amount at frequencies beyond about 1–2 Hz. Theoretical models for a massless rigid foundation under the excitation of an incoherent wave field predict the general trend of the estimated transfer function reasonably well over a large frequency range. The results of numerical examples show that the recorded response spectral attenuation of basement records at high frequencies with respect to the free-field is mainly caused by kinematic interaction, while the changes in storey shear and overturning moment in a structure due to soil flexibility are mainly the results of inertial interaction.     

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.     

Effects of wave passage on the relevant dynamic properties of structures with flexible foundation

An evaluation of the wave passage effects on the relevant dynamic properties of structures with flexible foundation is presented. A simple soil–structure system similar to that used in practice to take into account the inertial interaction effects by the soil flexibility is studied. The kinematic interaction effects due to non‐vertically incident P, SV and Rayleigh waves are accounted for in this model. The effective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free‐field ground motion. In this way, the maximum structural response could be estimated from standard free‐field response spectra using the period and damping of the building modified by both the soil flexibility and the travelling wave effects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil–structure systems to identify under which conditions the effects of wave passage are important. It comes out that these effects are generally negligible for the system period, but they may significantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the diffraction and scattering of the incident waves by the foundation. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic response of offshore structures in random seas

A study of the dynamic response of offshore structures to simultaneous loadings by random earthquake ground motions and random sea waves is presented. Emphasis is placed on the evaluation of dynamic soil-structure interaction effects and also on the evaluation of non-linear hydrodynamic damping effects due to sea waves for the seismic response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider's power spectrum and the Morison equation defines the wave forcing function. The Tajimi-Kanai power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency-domain random vibration approach. It is found that the first few vibrational modes contribute significantly to the dynamic response. The response due to earthquake loadings is larger when the soil-structure interaction effects are considered. The hydrodynamic damping forces are higher in random seas than in still water and sea waves reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquake forces.     

Response of tall buildings to base rocking induced by Rayleigh waves

By now, it is well known that long‐period surface waves can induce resonant response in high‐rise buildings, in particular those located in sedimentary basins. Rayleigh wave passage has been reported to induce rocking motion at the base of the buildings which can increase displacement demands significantly. However, the building behavior to base rocking has not been extensively studied because commercially available instruments do not record rotational components of ground motion, and thus, rocking time histories have not been available to the analysts. In a recent study, we proposed an effective method for estimating the rocking associated with Rayleigh waves, which takes into account their frequency‐dependent phase velocities. In the present work, we select a number of recorded seismic motions which include surface waves on sedimentary basins from recent well‐recorded earthquake events. Then, we proceed to identify and extract the recorded surface waves by using the technique mentioned above. Using realistic soil‐structure analytical models that have been proposed in the published literature for high‐rise buildings, we study their response to Rayleigh waves as they respond to both translational and rocking motions. Of particular interest is to compare the response of such structures with and without the presence of rotational motions due to surface waves. Using the roof displacement and the building interstory drift as response quantities, our results indicate that demands are controlled by rotational (rocking) motions associated with Rayleigh waves.     

On the interaction of rayleigh surface waves with structures

A two-dimensional soil-structure interaction analysis is carried out for transient Rayleigh surface waves that are incident on a structure. The structure is modelled by a three-degree of freedom rigid basemat to which is attached a flexible superstructure, modelled by a single mass-spring system. The structural responses to a given Rayleigh wave train are compared with those that would have been obtained if the free-field acceleration-time history had been applied as a normally incident body wave. The results clearly exhibit the [frequency filtering] effects of the rigid basemat on the incident Rayleigh waves. It is shown that, if seismic excitation of a structure is, in fact, due to Rayleigh surface waves, then an analysis assuming normally incident body waves can considerably over-estimate structural response, both at basemat level for horizontal and vertical motions and for vertical oscillations of the superstructure. However, in the examples considered here, relatively large rocking effects were induced by the Rayleigh waves, thus giving maximum horizontal accelerations in the superstructure that were of comparable magnitude for Rayleigh and normally incident body waves.     

Response of L-shaped rigid foundations embedded in a uniform half-space to traveling seismic waves

A simplified indirect boundary element method is applied to compute the impedance functions for L-shaped rigid foundations embedded in a homogeneous viscoelastic half-space. In this method, the waves generated by the 3D vibrating foundation are constructed from radiating sources located on the actual boundary of the foundation. The impedance functions together with the free-field displacements and tractions generated along the soil–foundation interface are used to calculate the foundation input motion for incident P, S and Rayleigh waves. This is accomplished by application of Iguchi's averaging method which, in turn, is verified by comparison with results obtained rigorously using the relation between the solutions of the basic radiation (impedance functions) and scattering (input motions) problems. Numerical results are presented for both surface-supported and embedded foundations. It is shown how the seismic response of L-shaped foundations with symmetrical wings differs from that of enveloping square foundations. The effects of inclination and azimuth of the earthquake excitation are examined as well. These results should be of use in analyses of soil–structure interaction to account for the traveling wave effects usually overlooked in practice.     

基础柔性对土-结构相互作用系统响应影响的一个解析解

采用波函数展开法,通过SH波入射均匀半空间中二维埋置半圆形刚柔复合基础-单质点模型,推导土-刚柔复合基础-上部结构动力相互作用的解析解,并验证解的正确性。研究表明:基础柔性对于系统响应峰值与系统频率有较大影响。考虑基础柔性后,上部结构相对响应峰值相比全刚性基础结果均有一定减小,且系统频率也会产生向低频偏移的现象。     

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.     

Scattering and diffraction of earthquake motions in irregular,elastic layers,II: Rayleigh and body P and SV waves

We present our study of the wave propagation in an irregularly layered, elastic wave-guide excited by incoming Rayleigh surface waves and P and SV body waves. Our aim is to show examples of applying a method that will make it possible to analyze the distribution and amplification of displacements, rotations, curvatures, strains, and stresses on or below the ground surface during passage of strong earthquake ground motion. We employ the weighted-residuals method, which makes it possible to calculate the scattered and diffracted waves, and then we illustrate the amplification of motions in the vicinity of inhomogeneity.     

Dynamic response of non-linear building-foundation systems

An analysis is made of the steady-state response of a bilinear hysteretic structure supported on the surface of a viscoelastic half-space. The method of equivalent linearization is used to solve the equations of motion, and simplified approximate formulas are obtained for the fundamental resonant frequency of the system and for an effective critical damping ratio. Numerical results indicate that for non-linear hysteretic structures compliance of the soil foundation may lead to larger displacements than would occur if the base were rigid. This behaviour differs from that generally observed for linear systems, for which the effect of soil-structure interaction is to reduce the rigid-base response.     

Parametric earthquake response of torsionally coupled buildings with foundation interaction

A study is made of the effect of soil-structure interaction on the coupled lateral and torsional responses of asymmetric buildings subjected to a series of historical free-field earthquake base motions. It sh shown that for particular classes of actual buildings the equivalent rigid-base responses are significantly increased for structures founded on medium-stiff soils, and hence the assumption of the major building codes that a conservative estimate of response is obtained by considering the structure to be fixed rigidly at its base is shown to be inconsistent with the presented dynamic results. It is shown that foundation interaction produces greatest amplification of torsional coupling effects for structures subjected to a particular class of European strong-motion earthquake records, identified by similarities in their spectral shape, for which the vibrational energy of the ground motion is distributed approximately uniformly over the range of frequencies which are of interest for real structures. It is recommended that provision be made in the torsional design procedures of building codes for the increase in the coupled torsional response due to soil-structure interaction as indicated in this study. Such provision should be based on the results of comprehensive parametric studies employing a wide selection of earthquake records and accounting for expected variations in localized soil conditions.     

The influence of dynamic soil–structure interaction on traffic induced vibrations in buildings

This paper deals with the dynamic response of buildings due to traffic induced wave fields. The response of a two-storey single family dwelling due to the passage of a two-axle truck on a traffic plateau is computed with a model that fully accounts for the dynamic interaction between the soil and the structure. The results of three cases where the structure is founded on a slab foundation, a strip foundation and a box foundation are calculated and a comprehensive analysis of the dynamic structural response is performed. A methodology is also proposed to calculate the structural response, neglecting the effects of dynamic soil–structure interaction. A comparison with the results of calculations where dynamic soil–structure interaction is accounted for shows that a good approximation is obtained in the case of a rigid structure resting on a soft soil.     

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.     

In-plane foundation-soil interaction for embedded circular foundations

Foundation soil interaction is studied using an analytical two-dimensional model, for circular foundations embedded in a homogeneous elastic half-space and for incident plane P- and SV- and for surface Rayleigh waves. The scattered waves are expanded in complete series of cyclindrical wave functions. A detailed analysis is presented of the foundation response to unit amplitude incident waves as a function of the type of incident waves and angle of incidence, the depth of the embedment and the foundation mass per unit length.It is shown that free-field translations and point rotation approximate well the foundation input motion only for very long incident waves. For shorter incident waves, those in general overestimate the foundation input motion. Neglecting the rotation of the foundation input motion (which is usually done in practice) may eliminate a major contribution to the base excitation of buildings and may cause nonconservative estimates of the forces in these buildings. Incident waves appear as ‘longer’ to a shallow foundation than to a deeper foundation. Therefore, deeper foundations are more effective in reflecting and scattering the short incident waves.