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1.
When modelling unbounded domains, formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance. In this paper, a method to describe the dynamic stiffness by a system of fractional differential equations in the time‐domain is presented. Here, a doubly asymptotic rational approximation of the low‐frequency force–displacement relationship is used, whereas a direct interpretation of the asymptotic part as a fractional derivative is possible. The numerical solution of the corresponding system of fractional differential equations is demonstrated using the infinite beam on elastic foundation as an example. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations 总被引：1，自引：1，他引：1
This paper compares the use of local and global shape functions in a boundary element method that is used in a prediction model for traffic induced vibrations. The boundary element formulation describes the interaction problem between a linear elastic layered half-space and a longitudinally invariant structure representing a road or a railway track. The boundary element formulation in the frequency–wavenumber domain is obtained by means of a weighted residual method. Constant element shape functions, as well as Legendre and Chebyshev shape functions are considered. Their effect on both accuracy and computational effort is investigated. The presence of a singularity in the Chebyshev based shape functions allows to obtain a better approximation for the soil tractions. The theory is applied to road traffic induced vibrations where the response is calculated in a large number of output points. 相似文献
3.
A first-order formulation to analyze the dynamic response of layered soil profiles is presented as an alternative to the widely used second-order thin-layer method by the direct stiffness approach, including an efficient simulation of the underlaying elastic half-space. In contrast to the thin-layer method where response is expressed through a combination of second-order propagation modes, the proposed procedure uses first-order modal parameters that have the capacity to provide a good approximation in the complete wave number domain k, including the exact stiffness values for k=0 and k→∞, thus justifying its designation of doubly-asymptotic. This feature allows obtaining the exact soil profile response for static loads, while the proposed treatment of the elastic half-space reproduces naturally the radiation condition without a need of artificial damping. The capacity of the proposed formulation to solve elastodynamic problems is assessed by comparing its results with those of exact solutions available in the literature, and numerical solutions of rigid disks supported on the surface of different soil profiles. 相似文献
4.
A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response. 相似文献
5.
Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media 
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下载免费PDF全文 Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms (Born/single scattering approximation) are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation (heterogeneous) medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps: firstly, to handle the forward scattering by taking into account the second-order Born approximation, which is related to generalized Radon transform (GRT) about quadratic scattering potential; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation ( \( \delta_{c}/c_{0} \) ) of background media up to 10 %, and its inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the perturbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a transmission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process. 相似文献
6.
The dynamic through–soil interaction between nearby pile supported structures in a viscoelastic half-space, under incident S and Rayleigh waves, is numerically studied. To this end, a three-dimensional viscoelastic BEM–FEM formulation for the dynamic analysis of piles and pile groups in the frequency domain is used, where soil is modelled by BEM and piles are simulated by one-dimensional finite elements as Bernoulli beams. This formulation has been enhanced to include the presence of linear superstructures founded on pile groups, so that structure–soil–structure interaction (SSSI) can be investigated making use of a direct methodology with an affordable number of degrees of freedom. The influence of SSSI on lateral spectral deformation, vertical and rotational response, and shear forces at pile heads, for several configurations of shear one-storey buildings, is addressed. Maximum response spectra are also presented. SSSI effects on groups of structures with similar dynamic characteristics have been found to be important. The system response can be either amplified or attenuated according to the distance between adjacent buildings, which has been related to dynamic properties of the overall system. 相似文献
7.
Christopher Bode Reinhold Hirschauer Stavros A. Savidis 《Soil Dynamics and Earthquake Engineering》2002,22(4)
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’. 相似文献
8.
In this paper, time domain dynamic analysis of piles under impact loading is presented. For this purpose a hybrid boundary element technique is implemented. Linear beam column finite elements are used to model the piles and resulting governing equations are solved using an implicit integration scheme. The continuum is assumed to be elastic and an efficient step-by-step time integration scheme is implemented by using an approximate half space integral formulation. By enforcing displacement equilibrium conditions at each time step, a system of equations is generated which yields the solution. Results of this time domain formulation under linear material behavior are compared with Laplace domain results to validate the methods. 相似文献
9.
Ru-Shan Wu 《Pure and Applied Geophysics》1996,148(1-2):155-173
When reverberations between heterogeneities or resonance scattering can be neglected but accumulated effects of forward scattering are strong, the Born approximation is not valid but the De Wolf approximation can be applied in such cases. In this paper, renormalized MFSB (multiple-forescattering single-backscattering) equations and the dual-domain expression for scalar, acoustic and elastic waves are derived by a unified approach. Two versions of the one-return method (using MFSB approximation) are given: One is the wide-angle dual-domain formulation (thin-slab approximation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be seen clearly that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, by impedance perturbations. The validity of the method and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface derived from numerical simulations by the wide-angle method match the theoretical curves well up to critical angles. For the reflections of a low-velocity slab, the agreement between theory and synthetics only starts to deteriorate for angles greater than 70°. The accuracy of the wide-angle version of the method could be further improved by optimizing the wave-number filtering for the forward propagation and shrinking the step length along the propagation direction. 相似文献
10.
A boundary element formulation having discontinuous curved quadratic elements is presented for 2D elastodynamics. The first fundamental solution for static case is subtracted from and added to the first fundamental solution for dynamic case. As both kernels have the same order of singularity, the integral involving the regular expression arising from the subtraction can be calculated. matrix is calculated by employing the well-known rigid-body motion technique. The formulation is performed in Fourier transform space. Based on the formulation presented in this study, a general purpose computer program is developed for elastic or visco-elastic 2D elastodynamic problems. The program performs the analysis in Fourier transform space and can also be used for static analysis by assigning a very small value close to zero for the frequency. The results of some elastodynamic and dynamic soil–structure interaction problems obtained using the present study are compared with those in the literature. 相似文献
11.
This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L2 norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method. 相似文献
12.
Transmitting boundary for water-saturated transversely isotropic strata based on the u–U formulation
A new transmitting boundary in a cylindrical coordinate system has been developed for modeling the elastic waves radiating out to an infinite boundary in water-saturated transversely isotropic soil strata over a rigid bedrock. The saturated soil strata are assumed to consist of a porous material and modeled as a transversely isotropic two-phase medium, based on the u−U formulation. The newly developed transmitting boundary is combined with the finite-elements model of the near-field region, using the same u−U formulation, and applied to the study of the dynamics of a rigid circular foundation in porous isotropic or transversely isotropic layered strata, either fully or partly saturated with water. The verification and application examples give valuable insights into new and interesting aspects of the dynamic behavior of rigid circular foundations in fully or partly saturated two-phase ground in terms of permeability, transverse anisotropy, and ground-water table level. 相似文献
13.
The transient response of large embedded foundation elements of length-to-diameter aspect ratio D/B=2–6 is characterized by a complex stress distribution at the pier–soil interface that cannot be adequately represented by means of existing models for shallow foundations or flexible piles. On the other hand, while three-dimensional (3D) numerical solutions are feasible, they are infrequently employed in practice due to their associated cost and effort. Prompted by the scarcity of simplified models for design in current practice, we here develop an analytical model that accounts for the multitude of soil resistance mechanisms mobilized at their base and circumference, while retaining the advantages of simplified methodologies for the design of non-critical facilities. The characteristics of soil resistance mechanisms and corresponding complex spring functions are developed on the basis of finite element simulations, by equating the stiffness matrix terms and/or overall numerically computed response to the analytical expressions derived by means of the proposed Winkler model. Sensitivity analyses are performed for the optimization of the truncated numerical domain size, the optimal finite element size and the far-field dynamic boundary conditions to avoid spurious wave reflections. Numerical simulations of the transient system response to vertically propagating shear waves are next successfully compared to the analytically predicted response. Finally, the applicability of the method is assessed for soil profiles with depth-varying properties. The formulation of frequency-dependent complex spring functions including material damping is also described, while extension of the methodology to account for nonlinear soil behavior and soil–foundation interface separation is described in the conclusion and is being currently investigated. 相似文献
14.
In this work the interaction between adjacent rigid, surface foundations resting on a viscoelastic layered soil medium is studied. A 3-D frequency domain BEM formulation in conjunction with infinite space fundamental solutions and the so called `successive stiffness method', initially developed for elastostatics and adapted here for the solution of elastodynamic problems, are used for the simulation of a layered soil medium. As a result, a discretization of the soil-foundation interface and the surrounding free surface as well as the soil layers' interfaces is necessary. However, it is shown in this work that reasonably accurate results can be obtained by using a substantially reduced discretization scheme involving only a small portion of the free surface surrounding the foundation and the corresponding interfaces of the soil layers. The presented numerical results demonstrate the importance of the dynamic foundation-soil-foundation interaction phenomenon which becomes even more pronounced where the supporting soil medium is made up of relatively shallow layers close to its free surface. 相似文献
15.
Dynamic response of high-speed ballasted railway tracks: 3D periodic model and in situ measurements 总被引：2，自引：0，他引：2
A three-dimensional (3D) model for the soil–railway track system is proposed. It is based on a geometrical periodic hypothesis. The dynamic soil–structure interaction is taken into account. This representation is used for the case of a ballasted railway track subjected to high-speed moving loads and a new formulation of dynamic responses of the system is proposed. Moreover, recent in situ measurements performed in a high-speed line of the North of France are presented. Lateral and vertical accelerations in several locations of the railway track have been measured and the periodic model is confronted with these records. 相似文献
16.
A new critical excitation method is developed for soil–structure interaction systems. In contrast to previous studies considering amplitude nonstationarity only, no special constraint of input motions is needed on nonstationarity. The input energy to the soil–structure interaction system during an earthquake is introduced as a new measure of criticality. It is demonstrated that the input energy expression can be of a compact form via the frequency integration of the product between the input component (Fourier amplitude spectrum) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for solving the critical excitation problem and deriving a bound on the earthquake input energy for a class of ground motions. The extension of the concept to MDOF systems is also presented. 相似文献
17.
In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction. 相似文献
18.
A soil medium at the side of an embedded structure is treated as mutually uncoupled horizontal layers of a unit thickness. A plane strain condition is assumed within each individual layer such that the medium responses do not vary along the thickness. According to previous work by the authors and also a new formulation given herein, the impedance of the above layer at the structure can be produced by frequency-independent simple mechanical models for all three modes of foundation responses. Similar frequency-independent models are also presented for the impedance at the foundation base. These models are made of two different basic elements and a mass interconnected in series. Their arrangements directly indicate the wiring of electric circuits which generate signals corresponding to the transient soil–structure interaction responses. To all intents and purposes, electric circuits do not loose time in responding to the inputs. Therefore, they allow us to simulate the soil–structure interaction response in shake table model tests, which are commonly conducted at relatively high excitation frequencies for earthquake simulation. 相似文献
19.
A stochastic approach has been formulated for the linear analysis of suspension bridges subjected to earthquake excitations. The transfer functions of various responses have been formulated while including the effects of dynamic Soil–Structure Interaction (SSI) via the use of the fixed-base modes of the structure. The excitation has been characterized by the ‘equivalent stationary’ processes corresponding to the free-field motions at each support and by an assumed coherency function between these motions. The proposed formulation considers the non-stationarity in the structural response due to sudden application of excitation by considering (i) the time-dependent frequency response functions, and (ii) the order statistics formulation for the peak factors in evolutionary response processes. The formulation has been illustrated by analysing the seismic response of the Golden Gate Bridge at San Francisco for two example excitations conforming to USNRC-specified design spectra. The significance of various governing parameters on the dynamic soil–structure interaction effects on the seismic response of suspension bridges has also been studied. It has been found that the contribution of the vertical component of ground motion to the bridge response increases with increasing soil compliance. Also, the extent to which the spatial variation of ground motion affects the bridge response depends on how significant the SSI effects are. Copyright © 1999 John Wiley & Sons Ltd. 相似文献
20.
R. Betti 《地震工程与结构动力学》1997,26(10):1005-1019
A boundary element formulation of the substructure deletion method is presented for the seismic analysis of the dynamic cross-interaction between multiple embedded foundations. This approach is particularly suitable for three-dimensional foundations of any arbitrary geometrical shape and spatial location, since it requires only the discretization of the foundations’ surfaces. The surrounding soil is represented by a homogeneous viscoelastic half-space while the foundations are assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes. The proposed methodology is tested for the case of two identical embedded square foundations for different values of the foundations’ embedment and distance. The effects of the cross-interaction are outlined in the components of the impedance matrix and of the foundation input motion. © 1997 John Wiley & Sons, Ltd. 相似文献