Soil–structure interaction for a SDOF oscillator supported by a flexible foundation embedded in a half-space: Closed-form solution for incident plane SH-waves

A closed-form analytical solution is presented for the dynamic response of a SDOF oscillator, supported by a flexible foundation embedded in an elastic half-space, and excited by plane SH waves. The solution is obtained by the wave function expansion method. The solution is verified for the special case of a rigid foundation by comparison with published results. The model is used to investigate the effect of the foundation flexibility on the system response. The results show that the effect is significant for both foundation response and structural relative response. For a system with more flexible foundation, the radiation damping is smaller, the foundation response is larger, especially for obliquely incident waves, while the structural relative response is smaller, and the system frequency shifts towards lower frequencies. This simple model may be helpful to obtain insight into the effects of soil–structure interaction for a slim structure on an extended flexible foundation.     

Torsional response of a rigid circular foundation on a saturated half-space to SH waves

An analytical approach is used to study the torsional vibrations of a rigid circular foundation resting on saturated soil to obliquely incident SH waves. Biot’s poroelastic dynamic theory is considered to characterize the saturated soil below the foundation, which is solved by Hankel transform later. In order to consider the scattering phenomena caused by the existence of the foundation, the total wave field in soil is classified into free-field, rigid-body scattering field and radiation scattering field. According to the classification of wave field and the mixed boundary-value conditions between the soil and the foundation, torsional vibrations of the foundation are formulated in two sets of dual integral equations. Then, the dual integral equations are reduced to Fredholm integral equation of the second kind to be solved. Combining with the dynamic equilibrium equations of the foundation, the expressions for the torsional vibrations of the foundation are obtained. Numerical results are presented to demonstrate the influence of excitation frequency, incident angle, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibrations of the foundation.     

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.     

Dynamic response of rectangular foundations to obliquely incident seismic waves

A study is made of the harmonic response of a rigid massless rectangular foundation bonded to an elastic half-space and subjected to the action of both external forces and obliquely incident plane seismic waves. The associated mixed boundary value problem is discretized and solved numerically. The results obtained indicate that the angle of incidence of the seismic wave has a marked effect on the nature and magnitude of the foundation response.     

Dynamic response of flexible strip-foundations by boundary and finite elements

A time domain Boundary Element-Finite method is employed to determine the dynamic response of flexible surface two-dimensional foundations under conditions of plane strain placed on an elastic soil medium and subjected either to transient external forces or to obliquely incident seismic waves. The elastic, isotropic, and homogeneous soil medium is treated by the time domain Direct Boundary Element Method, while the flexible foundation is treated by the Finite Element Method. The two methods are appropriately combined through equilibrium and compatibility considerations at the soil-foundation interface. Parametric studies examining the effect of the relative stiffness between the foundation and the soil and the spatial distribution of the dynamic disturbances on the foundation response are presented.     

Response of a circular foundation on a uniform half-space to elastic waves

An alternative technique to obtain the dynamic response of a massless rigid circular foundation resting on a uniform elastic half-space when subjected to harmonic plane waves is presented. The technique relies on the use of an integral representation involving the free-field ground motion and the contact tractions obtained in the course of calculating the dynamic force–displacement relationship of the foundation for external forces. Tables listing the translational and rotational components of the response of the foundation for non-vertically incident SH, P, SV and Rayleigh waves are presented.     

Natural and accidental torsion in one‐storey structures on elastic foundation under non‐vertically incident SH‐waves

Factors α and β used in equivalent static analysis to account for natural and accidental torsion are evaluated with consideration of soil–structure interaction. The combined torsional effects of structural asymmetry and foundation rotation are examined with reference to a single monosymmetric structure placed on a rigid foundation that is embedded into an elastic half‐space, under to the action of non‐vertically incident SH waves. Dynamic and accidental eccentricities are developed such that when used together with the code‐specified base shear, the resulting static displacement at the flexible edge of the building is identical to that computed from dynamic analysis. It is shown that these eccentricities do not have a unique definition because they depend on both the selection of the design base shear and the criterion used for separation of the torsional effects of foundation rotation from those of structural asymmetry. Selected numerical results are presented in terms of dimensionless parameters for their general application, using a set of appropriate earthquake motions for ensuring generality of conclusions. The practical significance of this information for code‐designed buildings is elucidated. Copyright © 2006 John Wiley & Sons, Ltd.     

Code design provisions for torsionally coupled buildings on elastic foundation

The effectiveness of the design recommendations made by various major building codes to account for torsional coupling effects is evaluated with respect to the parametric responses to earthquake ground motion of a simple single-storey asymmetric building model supported on an elastic foundation. The objectives are to determine the extent to which the response trends observed in previous studies of asymmetric rigidly based buildings are affected by changes in the flexibility of the foundation medium and to comment on and suggest necessary amendments to the design recommendations in order that suitable allowance be made for the resultant changes in the magnitude of torsional coupling effects. It is concluded that whilst the qualitative effects of torsional coupling are not affected by soil–structure interaction, their magnitude depends significantly on the frequency content of the free-field motion. The response to the El Centro earthquake record is conservatively accounted for by assuming the structure to be supported on a rigid foundation. An allowance for increased response effects due to soil–structure interaction is suggested for incorporation in the torsional design recommendations when European earthquake records are employed.     

Dynamic analysis of 3-D flexible embedded foundations by a frequency domain BEM-FEM

A study on the dynamic response of three-dimensional flexible foundations of arbitrary shape, embedded in a homogenous, isotropic and linear elastic half-space is presented. Both massive and massless foundations are considered. The soil-foundation system is subjected to externally applied forces, and/or to obliquely incident seismic waves. The numerical method employed is a combination of the frequency domain Boundary Element Method, which is used to simulate the elastic soil medium, and the Finite Element Method, on the basis of which the stiffness matrix of the foundation is obtained. The foundation and soil media are combined by enforcing compatibility and equilibrium conditions at their common interface. Both relaxed and completely bonded boundary conditions are considered. The accuracy of the proposed methodology is partially verified through comparison studies with results reported in the literature for rigid embedded foundations.     

Out-of-plane (SH) soil-structure interaction: Semi-circular rigid foundation revisited

The model studied in this paper presents an extension of previous work for a shear wall on a semi-circular rigid foundation in an isotropic homogeneous and elastic half-space. The objective is to develop a soil-structure interaction model that can later be applied to the case of a flexible foundation. As shown in the Introduction below, Luco considered the case of a rigid foundation subjected to vertical incident plane SH waves, and Trifunac extended the solution for the same rigid foundation subjected to SH waves but for arbitrary angles of the incidence. In this paper, a new approach and model are presented for the same semi-circular rigid foundation with a tapered-shape (instead of rectangular) superstructure. The analytical expression for the deformation of the semi-circular rigid foundation below this tapered shear wall with soil-structure interaction in an isotropic homogeneous and elastic half-space is thus derived. Results are then compared with those of Trifunac discussed in the section below. This problem formulation can and will later be extended in the case of a flexible foundation that is semi-circular or arbitrarily shaped.     

Effects of the site dynamic characteristics on soil–structure interaction (I): Incident SH-Waves

In this paper, the role that the site dynamic characteristics play in soil–structure interaction is studied on a simple model in which the site is represented as a soil layer over bedrock (half-space), and using the indirect boundary-element method (IBEM). For the purpose of comparison with published analytical solutions, the structure is represented as a shear wall supported by a semi-circular rigid foundation, subjected to incident plane SH waves. The accuracy of the method is verified, numerical results are analyzed, and the model response is compared with earthquake observations at the Hollywood Storage Building. It is shown that the effects of dynamic soil–structure interaction may become more significant near the characteristic frequencies of the site, and that the resonance of the system shifts to lower frequencies. The thickness of the soil layer, the stiffness of the bedrock, and the mass and the stiffness of the superstructure all influence the values of the system frequencies and system amplitudes.     

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.     

弹性层状半空间中无限长洞室对斜入射 平面SH波的三维散射(Ⅱ) 数值结果与分析

以基岩上单一土层场地为例, 计算分析了在斜入射平面SH波作用下弹性层状半空间中无限长洞室附近的地表位移. 研究表明, 层状半空间中地下洞室对波的散射与均匀半空间情况存在显著差别. 层状场地由于考虑了场地自身的动力特性, 使得洞室附近地表位移幅值的空间变化更为复杂, 基岩与土层刚度比、 土层厚度对散射效应均有着重要影响. 随着基岩与土层刚度比的增大, 地表位移幅值整体上逐渐增大; 随着土层厚度的增大, 土层对地表位移幅值的影响逐渐减小. 在频域解答的基础上, 给出了层状半空间中洞室对斜入射SH波散射的时域解答, 并以Ricker波为例进行了数值计算.      

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.     

A note on the dynamic response of rigid embedded foundations

The problem of the dynamic response of rigid embedded foundations subjected to the action of external forces and seismic excitation is analysed. It is shown that to calculate the response of rigid embedded foundations, or the response of flat rigid foundations subjected to non-vertically incident seismic waves, it is necessary to obtain not only the impedance matrix for the foundation, but also the forces induced by the incident seismic waves. Under these general conditions, rocking and torsional motion of the foundation is generated in addition to translation. The case of a two-dimensional rigid foundation of semi-elliptical cross-section is used as an example to illustrate the effects of the embedment depth and angle of incidence of the seismic waves on the response of the foundation.     

Structural response for stochastic kinematic interaction

The influence of stochastic kinematic interaction (SKI) on structural response is investigated in this paper. The SKI is evaluated through a computational model based on the boundary element method (BEM) formulated in the frequency domain. The singular integrals required in the computation of BEM are evaluated in a closed form. It is assumed that the foundation input motion (FIM) is the result of the superposition of many plane, stationary, correlated stochastic SH‐, P‐ and SV‐waves travelling within a homogeneous viscoelastic soil at different angles. The results obtained indicate that the effect of SKI on the foundation response is qualitatively similar to that of wave passage. Both effects involve a reduction of translational components of the response at intermediate and high frequencies and creation of a rotational response component at intermediate frequencies, which decreases at high frequencies. While, it is found that the SKI decreases the maximum response of structures built on embedded rigid strip foundations excited by SH‐ and P‐waves, it increases the maximum response for SV‐waves, except when the natural frequency of the structure is less than 0.5 Hz and for short structures excited by shallowly incident SV‐waves. Copyright © 2001 John Wiley & Sons, Ltd.     

Lateral response of dams in semi-elliptical rigid canyons

An analytical closed-form solution is developed for the lateral response of earth and rockfill dams built in semi-elliptical canyons. The dam is idealized as a linearly hysteretic elastic body deforming only in shear, whereas the canyon is assumed to be rigid. The solution for the dam response is given in terms of prolate spheroidal radial and angular functions of the first kind and zero order. Results are presented for natural frequencies, modal displacement shapes, participation factors, and response to transient and steady-state harmonic base excitation for various dam length-to-height ratios. Comparisons are made of the effects of the length-to-height ratio and the canyon shape on the response of dams built in semi-elliptical and rectangular canyons. A subsequent study (Dakoulas, P. & Hsu, C.H., Response of earth dams in semi-elliptical flexible canyons to oblique SH waves, Report, Rice University, Houston, Texas, 1993) extends this model to a semi-elliptical canyon consisting of flexible elastic rock, subjected to obliquely incident harmonic SH waves.     

The effect of foundation flexibility variation on system response of dynamic soil–structure interaction: an analytical solution

A closed-form analytical solution is presented for the dynamic response of a SDOF oscillator, supported by a flexible composite foundation embedded in an elastic half-space, and excited by plane SH waves. The solution is obtained by the wave function expansion method. The solution is verified for the two limiting cases of a rigid–flexible composite foundation and a homogeneous flexible foundation by comparison with published results. The model is used to investigate the effect of the foundation flexibility variation on the system response. The results show that the effect is significant for both foundation response and structural relative response. For a system with larger foundation flexibility variation, the peak of the foundation effective input motion is smaller, while the amplitude of structural relative response less changes. When foundation flexibility variation decreases, system frequency will shift to lower frequency, and the shift value is also highly dependent on the foundation flexibility variation.     

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。     

Dynamic soil–structure interaction effects on the seismic response of asymmetric buildings

An approach is formulated for the linear analysis of three-dimensional dynamic soil–structure interaction of asymmetric buildings in the time domain, in order to evaluate the seismic response behaviour of torsionally coupled buildings. The asymmetric building is idealized as a single-storey three-dimensional system resting on different soil conditions. The soil beneath the superstructure is modeled as linear elastic solid elements. The contact surface between foundation mat and solid elements of soil is discretised by linear plane interface elements with zero thickness. An interface element is further developed to function between the rigid foundation and soil. As an example, the response of soil–structure interaction of torsionally coupled system under two simultaneous lateral components of El Centro 1940 earthquake records has been evaluated and the effects of base flexibility on the response behaviour of the system are verified.