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1.
A semi-analytical model for the evaluation of dynamic impedance of rigid surface footing bonded to multi-layered subsoil is proposed. The technique is based on the dual vector form of wave motion equation and Green's influence function of subdisk for horizontally layered half-space. The multi-layered half-space is divided into a quite large number of mini-layers and the precise integration method (PIM) is introduced for the numerical implementation. The PIM is highly accurate for solving sets of first-order ordinary differential equations with specified two-end boundary conditions. It can produce numerical results of Green's influence functions up to the precision of computer used. The dual vector form of wave motion equation makes the combination of two adjacent mini-layers/layers very easy. As a result, the computational effort for the evaluation of Green's influence function of the multi-layered half-space is reduced to a great extent. In order to satisfy the mixed boundary condition at the surface, the footing–soil interface is discretized into a number of uniformly spaced subdisk-elements. Comparisons illustrating the efficiency and accuracy of the proposed approach are made with a number of solutions available in the literature. 相似文献
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A study is carried out to evaluate dynamic response of an elastic circular cylindrical tank having a rigid base under a vertical excitation taking into consideration the interaction with the foundation soil. At first, the soil is represented by frequency-independent parameters. Two coupled differential equations, governing the motion of the shell and the base, are solved using a step by step integration technique. The hydrodynamic pressures, acting on the shell and on the base, are derived from a velocity potential function which satisfies the Laplace equation and the appropriate boundary conditions. The response of the simplified model of a tank having a rigid base on a stiff foundation soil is compated to that obtained elsewhere to check the accuracy of the present model. Reasonable agreement is found between the maximum wall displacement and the associated stresses with those found by a more elaborate model. The interaction of the tank and the soil reduces the response than that calculated under the assumption of a rigid foundation soil. A parametric study to examine the effects of the height-to-radius ratio of the tank, and the effects of the shear wave velocity of the soil on the response is conducted. Varieties of foundation models are used to assess the sensitivity of the response to the variation in the soil parameters. Finally, a more representative solution for the problem in the frequency domain is obtained where the soil is appropriately modelled by frequency-dependent parameters. The transfer functions of the response of the tank wall and of the relative base motion are evaluated, and a comparison between the frequency-dependent and the frequency-independent solutions is made. 相似文献
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The precise integration method (PIM) is proposed for the dynamic response analysis of rigid strip footing resting on arbitrary anisotropic multi-layered half-space. In the frequency domain, the governing equation of wave motion is converted into dual vector form of first-order ordinary differential equations which is solved by PIM. Each layer is divided into a large number (say, 2N) of mini-layers of equal thickness, within which characteristic matrices are assumed to vary following the Taylor series expansion to the fourth order. As a result, any desired accuracy of the displacements and stresses can be achieved by PIM. In addition, dual vector form equation makes it quite easily to combine two adjacent mini-layers into a new one. Each pass of combination reduces the total number of mini-layers by a half. The computational effort for the evaluation of the dynamic impedance of rigid strip footing can be reduced to a great extent. Numerical examples are provided to validate the efficiency and accuracy of the proposed approach. 相似文献
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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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This paper shows an effective implementation of the half-plane Green function for surface strip impulses (Lamb's problem), which was previously developed in a closed form by the authors, into the time-domain boundary element method for the analysis of related initial boundary value problems. The time-stepping algorithm utilizing Heaviside step function makes the solution process free from the Rayleigh wave front singularity. Illustrative analyses performed include that: First, the response due to an impulsive uniform strip loading is dealt with in order to check the accuracy of the present solution and to interpret the associated wave motion in the medium. Second, a rigid massless strip surface foundation is analysed when subjected to various impulsive loadings in vertical, horizontal and rotational directions to observe which wave is most concerned with the respective foundation motion. The field response is also of interest with respect to distance attenuation. Third, the dynamic cross-interaction between active and passive foundations through soil is investigated when multiple strip foundations are placed separately on a half-space with a certain distance. 相似文献
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A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure. 相似文献
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Baranov proposed an approach for the treatment of the subgrade in the dynamic response analysis of a rigid foundation which is partially embedded. The approach is based on a Winkler approximation together with wave equation solutions developed for simplified conditions. The paper extends and modifies Baranov's approach so as to be applicable to surface foundation problems, by introducing an internal coupling mechanism. Closed form expressions are presented for the steady state harmonic responses of a massless rigid footing and an elastic beam on the surface of the presented subgrade model. These expressions can accommodate the inhomogeneity of the subgrade in a straightforward manner. The model is found to perform well in reproducing the continuous subgrade medium behaviour. The dynamic responses of structures are often highly dependent on the subgrade modelling and therefore great caution is needed in modelling the subgrade. 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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We propose a wave scattering approach to the problem of deconvolution by the inversion of the reflection seismogram. Rather than using the least-squares approach, we study the full wave solution of the one-dimensional wave equation for deconvolution. Randomness of the reflectivity is not a necessary assumption in this method. Both the reflectivity and the section multiple train can be predicted from the boundary data (the reflection seismogram). This is in contrast to the usual statistical approach in which reflectivity is unpredictable and random, and the section multiple train is the only predictable component of the seismogram. The proposed scattering approach also differs from Claerbout's method based on the Kunetz equation. The coupled first-order hyperbolic wave equations have been obtained from the equation of motion and the law of elasticity. These equations have been transformed in terms of characteristics. A finite-difference numerical scheme for the downward continuation of the free-surface reflection seismogram has been developed. The discrete causal solutions for forward and inverse problems have been obtained. The computer algorithm recursively solves for the pressure and particle velocity response and the impedance log. The method accomplishes deconvolution and impedance log reconstruction. We have tested the method by computer model experiments and obtained satisfactory results using noise-free synthetic data. Further study is recommended for the method's application to real data. 相似文献
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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. 相似文献
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The objective of the present approach is to determine the structural response to external force excitations and earthquake excitations with consideration of soil-structure interaction. The physical model concerned is a flexible structure resting on a rigid or flexible foundation embedded in a layered soil medium. The vibration of the structure is first analyzed using the wave propagation approach without reference to the interaction. The interaction effect is recovered by the impedance relationship developed in the companion paper. In an attempt to use the free field ground motion as the input to the system, the Maxwell's reciprocal theorem is applied to remedy the difference between the free field and real ground motion in the presence of the structure. As a result, the structural response at any location is written as a linear function of external excitations and the seismic source. Such a solution form is convenient for statistical analysis. 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
14.
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. 相似文献
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Soil‐structure system frequency and damping: Estimation from eigenvalues and results for a 2D model in layered half‐space 
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下载免费PDF全文 This paper presents a formulation for estimation of the frequency and damping of a soil‐structure interaction system based on the classical modal analysis and solving the system eigenvalue problem. Without loss of generality, the structure is represented by a single degree of freedom oscillator, while the soil effects are included through impedance functions for in‐plane motion of a 2D rigid foundation. For the results presented in this paper, the impedance functions were computed by the indirect boundary element method for a rectangular foundation embedded in a soil layer over elastic bedrock. The study shows that the classical modal‐analysis approach works well, with the exception of squat, stiff structures, even though the impedance functions are frequency‐dependent and the soil‐structure interaction system does not possess normal modes. The study also shows that system frequency and damping are independent of the wave passage effects, contrary to findings of some previous studies, and that the site conditions, represented by the soil‐layer thickness and stiffness contrast between bedrock and soil layer, have significant influences on both system frequency and system damping. Finally, the paper examines the accuracy of some of the simple methods for estimation of these two system parameters and comments on some conflicting conclusions of previous studies about the effects of foundation embedment. 相似文献
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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. 相似文献
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Introduction In linear elastic medium,motion equation for lumped-mass finite element simulation of wave motion is expressed as(LIAO,2002)∑=+lililii ttGtM)()()(FUU&&(1)where Mi is lumped-mass at node i,Gil is stiffness coefficient of node i with respect to node l,üi(t)is acceleration vectors at node i,Ul(t)is displacement vectors at node l,Fi(t)is the external nodal force vectors acting at node i.If acceleration vectorsüi(t),displacement vectors Ul(t)and the external nodal force vectors… 相似文献
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Harmonic wave response of two 3-D rigid surface foundations 总被引：1，自引：0，他引：1
A boundary element methodology is developed for studying the response of a system of two rigid, massless or massive, surface foundations of arbitrary plan-forms to various harmonic waves under three-dimensional conditions. The method employs the frequency domain Green's function for the surface of the elastic half-space, thereby restricting the discretization only to the soil-foundation interfaces, and isoparametric quadratic quadrilateral boundary elements for increased accuracy. Extensive comparison studies with other known numerical solutions confirm the high accuracy of the proposed method. Detailed parametric studies are conducted in order to study the harmonic wave response of two square foundations as a function of the kind of incident wave, the angles of wave incidence, the wave frequency, the separation distance between the foundations and the amount of mass in each foundation and compare it against that of a single foundation for assessing the through the soil coupling effect. 相似文献