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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. 相似文献
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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. 相似文献
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The response of a rigid rectangular foundation block resting on an elastic half-space has been determined by considering first the displacement functions for any position on the surface of an unloaded half-space due to a harmonic point force. The influence of the foundation has been taken into account by assuming a relaxed condition at the interface, i.e. a uniform displacement under the foundation and that the sum of the point forces must equal the total applied force. The three motions of vertical, horizontal and rocking have been considered and numerical values for the in-phase and the quadrature components of the displacement functions are presented for a Poisson's ratio of 0.25. The effect of the mass and inertia of the foundation can be allowed for by an impedance matching technique. Response curves and non-dimensional resonant frequency curves are given for a square and a rectangular foundation for different mass and inertia ratios and for several values of Poisson's ratio. These curves are for design purposes and are an addition to similar published curves for circular and infinitely long rectangular foundations. Some of the calculated results have been verified by a laboratory experiment. 相似文献
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An approximate numerical procedure for calculation of the harmonic force-displacement relationships for a rigid foundation of arbitrary shape placed on an elastic half-space is presented. This procedure is used to evaluate the vertical, rocking and horizontal compliance functions for rigid rectangular foundations and the vertical compliance for a rigid square foundation with an internal hole. Several comparisons between the results obtained by the proposed approach and other methods are also presented. 相似文献
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This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations. 相似文献
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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. 相似文献
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A five-parameter discrete model that approximates the dynamic force4isplacement relationship for rigid foundations undergoing vertical vibrations on a uniform elastic half-space is presented. The model involves a combination of two springs, two viscous dampers and a mass. Values of the parameters for circular, square and rectangular foundations placed on the surface or embedded in an elastic half-space are listed. The parameters are obtained by minimizing the discrepancy between the force4isplacement relation for the model and that obtained by solution of the mixed boundary-value problem of the rigid foundation on an elastic half-space. The definition of an appropriate input motion to represent wave excitation is also discussed. The input motion to the discrete model differs from the input motion that should be used in a continuum model. 相似文献
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Christos Vrettos 《地震工程与结构动力学》1999,28(12):1525-1540
The vertical and rocking response of rigid rectangular foundations resting on a linear-elastic, compressible, non-homogeneous half-space soil model is studied. The non-homogeneity is described by a continuous yet bounded increase of shear modulus with depth. The mixed boundary value problem is solved by means of the semi-analytical method of the subdivision of the foundation/soil contact area whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green's functions for the particular soil model. Impedance functions are given for representative values of the non-homogeneity parameters, the Poisson's ratio and the foundation geometry over a wide range of frequencies. Significant features associated with the soil non-homogeneity are pointed out. Copyright © 1999 John Wiley & Sons Ltd. 相似文献
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Asymmetric steady-state structure-media interaction due to obliquely incident body waves is investigated via a version of the global local finite element method. In the present version, a local region that houses an axisymmetric structure is modelled by conventional finite elements, while the behaviour in the remaining portion of the homogeneous semi-infinite medium is presented by the spherical harmonics that are the eigensolutions of the entire space problem. The solution scheme involves (1) full displacement and traction continuity along the boundary between the local and the exterior regions and (2) satisfaction of the traction-free requirement on the surface of the half-space beyond the discretized region by virtue of a sequence of integral constraints of the non-zero weighted surface tractions of the spherical harmonics. The numerical results presented are for a perfectly bonded rigid circular foundation resting on the surface of the half-space and subjected to obliquely incident body waves. Dependence of the displacement response of the footing upon incident angles and dimensionless wave numbers is thoroughly studied. 相似文献
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Gin-Show Liou 《地震工程与结构动力学》1991,20(12):1115-1125
Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed. 相似文献
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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. 相似文献
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A simplified damped oscillator model is proposed to simulate unbounded soil for the vertical vibration analysis of rigid embedded foundations. Based on the dynamic responses of a foundation–soil system, an optimal equivalent model is determined as the best simplified model. Magnification responses of a foundation–soil system simulated by the optimal equivalent model are well consistent with those obtained by the half-space theory and by a widely used computer program even as embedment depth or vibrating mass increases. The optimal equivalent model utilizing only three parameters can result in responses as accurate as the existing models, which use more parameters. This proposed method uses much simpler procedure than optimization techniques used by most existing discrete models. This proposed method may also be easily and accurately applied to practical soil–structure interaction analysis. 相似文献
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This paper is concerned with the dynamic response of rigid strip foundations of arbitrary geometry embedded in a homogeneous elastic half-space. The embedded rigid foundation is modelled by an equivalent domain in a uniform half-space which is subjected to an appropriate body force field. The components of the impedance matrix are determined through the solution of a linear simultaneous equation system which is established by invoking rigid body displacements of discrete locations within the equivalent domain and appropriate equilibrium consideration. It is found that high numerical efficiency and flexibility can be achieved using the body force model when compared to boundary integral formulations through the selection of appropriate displacement influence functions and a ‘parent domain’ in the analysis. Numerical results are presented to illustrate the influence of the embedment ratio, frequency of excitation, foundation geometry and Poisson's ratio on the vertical, horizontal, rocking and coupled impedances of a single embedded foundation. The effect on the impedance due to the presence of an adjacent embedment is investigated for various distances between foundations and embedment ratios. 相似文献
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《地震工程与结构动力学》2018,47(5):1229-1249
This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios. 相似文献
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This paper examines the axisymmetric torsional vibrations of an elastic pile and a hemispherical foundation embedded in a homogeneous elastic half-space. The embedded foundation–half-space system is decomposed into an extended half-space and a fictitious foundation. The deformations of the fictitious system are specified by an admissible function containing a set of generalized coordinates. The Lagrangian equations of motion are used to determine these coordinates associated with the assumed displacement function. Numerical results are presented for torsional impedance of an elastic pile and a hemisphere to illustrate the effects of relative flexibility and geometry. By employing certain simplifications on the pile–half-space system an approximate closed form solution is presented for the torsional impedance of an elastic pile. 相似文献
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An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd. 相似文献
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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. 相似文献
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An approximate method for the analysis of the dynamic interaction between a flexible rectangular foundation and the soil with consideration of the out-of-plane deformation of the foundation is presented. The procedure is based on an extension of the subdivision method developed by Wong and Luco for rigid foundations. Numerical results describing the influence of the flexibility of the foundation on the vertical and rocking impedance functions and on the contact stresses between the foundation and the soil are presented. The possibility of representing a flexible foundation by an equivalent rigid foundation having the same force-displacement relationships is also discussed. The results obtained indicate that at low frequencies, the dynamic stiffness coefficients for flexible foundations are lower than those for a rigid foundation of the same area. At higher frequencies the opposite behaviour is observed. The radiation damping coefficients for flexible foundations are significantly lower than those for a rigid foundation of the same area. 相似文献