共查询到20条相似文献，搜索用时 15 毫秒
1.
A computationally efficient boundary integral equation technique to calculate the dynamic response of a group of rigid surface foundations bonded to a layered viscoelastic half-space and subjected to external forces and seismic waves is presented. The technique relies on an iterative scheme which minimizes in-core memory requirements and takes advantage of any geometrical symmetry of the foundations. Extensive results for the case of two rigid square foundations placed at different separations and bonded to a viscoelastic half-space are presented. It was found that the choice of discretization of the foundations has a marked effect on the calculated impedance functions for extremely small separations. Illustrative results for a case of several closely-spaced foundations bonded to a layered half-space are also presented. 相似文献
2.
An integral equation technique to determine the response of foundations embedded in a layered viscoelastic half-space when subjected to various types of seismic waves is presented. The technique is validated by comparison with previous results for rigid hemispherical and cylindrical foundations embedded in a uniform half-space. Illustrative results for rigid cylindrical foundations embedded in layered media are also presented. 相似文献
3.
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
4.
T. Senjuntichai S. Mani R.K.N.D. Rajapakse 《Soil Dynamics and Earthquake Engineering》2006,26(6-7):626-636
This paper considers time-harmonic vertical vibration of an axisymmetric rigid foundation embedded in a homogeneous poroelastic soil. The soil domain is represented by a homogeneous poroelastic half space that is governed by Biot's theory of poroelastodynamics. The foundation is subjected to a time-harmonic vertical load and is perfectly bonded to the surrounding half space. The contact surface can be either fully permeable or impermeable. The dynamic interaction problem is solved by employing an indirect boundary integral equation method. The kernel functions of the integral equation are the influence functions corresponding to vertical and radial ring loads, and a ring fluid source applied in the interior of a homogeneous poroelastic half space. Analytical techniques are used to derive the solution for influence functions. The indirect boundary integral equation is solved by using numerical quadrature. Selected numerical results for vertical impedance of rigid foundations are presented to demonstrate the influence of poroelastic effect, foundation geometry, hydraulic boundary condition along the contact surface and frequency of excitation. 相似文献
5.
The boundary element method is used to obtain dynamic stiffness functions of rigid cylindrical foundations embedded in a uniform or layered viscoelastic half-space. Dynamic stiffness functions of hemispherical foundations embedded in a uniform half-space are also computed. The direct integral equation formulation is used in combination with the complete space point load fundamental solution that is integrated numerically along the azimuthal coordinate. The approach is easy to implement because of the simplicity of the fundamental solution. The numerical results obtained by this method for cylindrical and hemispherical foundations are very close to corresponding published results obtained by different procedures. A parametric study shows the important effects of the Poisson's ratio on the dynamic stiffness functions of cylindrical foundations embedded in a uniform viscoelastic half-space. The effect of the bedrock compliance on the stiffness functions is also shown in the case of cylindrical foundations embedded in a soil layer that rests on a bedrock. 相似文献
6.
A new experimental method using a finite soil model with no special treatement on its boundaries is employed for soil-structure intration problems to simulate the semi-infinitenesss of the actual soil medium. The present method utlizies the characteristics of transient response to an impluse load to obtain the impedance functions and effective input motions for surface and embedded foundations. This technique is applicable to a linear elastic system whose impulse response decreases to a small enough value before observing the reflected waves. The experimentally obtained impedance functions and effective input motions are compared with those obtained by the direct boundary integral equation method and the hybrid approach. Good agreement between the xperimental and analytical results validates the present method as well as the accuracy of the numerical tools. 相似文献
7.
Piecewise heterogeneous media that the earth presents are composed of large-scale boundary structures and small-scale volume heterogeneities. Wave propagation in such piecewise heterogeneous media can be accurately superposed through the generalized Lippmann–Schwinger integral equation (GLSIE). Two different Born series modeling schemes are formulated for the boundary–volume integral equation with 2-D antiplane motion (SH waves). Both schemes decompose the resulting boundary–volume integral equation matrix into two parts: the self-interaction operator handled with a fully implicit manner, and the extrapolation operator approximated by a Born series. The first scheme associates the self-interaction operator with each boundary itself and the volume itself, and interprets the extrapolation operator as the cross-interaction between each boundary and other boundaries/volume scatterers in a subregion. The second scheme relates the self-interaction operator to each boundary itself and its cross-interaction with the volume scatterers on both sides, and expresses the extrapolation operator as both the direct and indirect (through the volume scatterers) cross-interactions between different boundaries in a subregion. By eliminating the displacement field from the volume scatterers, the second scheme reduces the dimension of the resulting boundary-volume integral equation matrix, leading to a faster convergence than the first scheme. Both the numerical schemes are validated by dimensionless frequency responses to a heterogeneous alluvial valley with the velocity perturbed randomly in the range of ca 5–20 %. The schemes are applied to wave propagation simulation in a heterogeneous multilayered model by calculating synthetic seismograms. Numerical experiments, compared with the full-waveform numerical solution, indicate that the Born series modeling schemes significantly improve computational efficiency, especially for high frequencies. 相似文献
8.
9.
Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green’s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method. 相似文献
10.
We present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi-static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi-conjugate gradient stabilizer was utilized with block incomplete lower-upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi-analytical solution. It also revealed that the use of a quasi-analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure. 相似文献
11.
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
12.
Peter Furness 《Geophysical Prospecting》1996,44(1):27-40
Modelling the theoretical response of several important geophysical systems involves the solution of Poisson's equation with homogeneous Neumann boundary conditions (i.e. a zero normal gradient) imposed over either open or closed surfaces. A simple integral equation solution to this problem is derived from first principles. It is applicable to both types of surface and in this respect represents an improvement on existing integral equation techniques. However, the present surface integral equation displays a strong singularity of order 1/R3 which requires an appropriate interpretation for its implementation. A comparison of some numerical results with analytical data taken from the literature demonstrates that the proposed integral equation technique is suitably robust, accurate and efficient for practical application in geophysical interpretation. 相似文献
13.
A versatile integral equation technique for magnetic modelling 总被引：1，自引：0，他引：1
Peter Furness 《Journal of Applied Geophysics》1999,41(4):737
A requirement currently exists in both mineral exploration and environmental or engineering geophysics for a technique to model the magnetic fields caused by bodies with large to extreme susceptibilities in which both induced and remanent magnetizations are significant. It is well known that modelling such magnetic fields is not amenable to any known approximation. It is a significantly difficult task that requires the solution of a magnetostatic boundary value problem. Analytical solutions to the problem are extremely useful for providing insight but generally of limited application in practical interpretation due to the geometrical complexity of real situations. Available numerical solutions include both volume and surface integral equation formulations. However neither of these are particularly efficient for the purpose. An alternative surface integral equation formulation is presented here which represents the required magnetic field in terms of a double layer over the surface of the body. The technique accommodates both remanent and induced magnetization and is generally applicable to any 3D body in a magnetic environment for which the Green's function is available. The present technique has significant advantages over other integral equation solutions in the geophysical literature. It is particularly economic in terms of the density of the surface discretization and consequently the computational effort. Moreover, it is extremely robust. It is found to yield accurate solutions for the type of thin bodies that cause numerical instability with other surface integral equation approaches. 相似文献
14.
本文用边界单元法模拟二维地形对大地电磁场的影响.首先用格林公式将二维大地电磁的边值问题转变成积分方程,然后用边界单元法解积分方程,得到地形上的大地电磁场和它的法向导数,由此可计算电阻率.与有限单元法相比,本方法剖分后的地形与实际地形的拟合程度高,向计算机输入原始数据的工作简单,可以在微机上计算地形引起的视电阻率.本方法适合于在野外生产现场进行大地电磁法的地形改正.计算表明,地形对H_x型波的影响比对E_x型波严重得多;随着周期的增长,地形对H_x型波的影响变得稳定. 相似文献
15.
16.
This paper proposes a coupled fluid layer–foundation–poroelastic half-space vibration model to study how still water affects foundations operating underwater. As an example, we consider the problem of the vertical vibration of a rigid disk on a poroelastic half-space covered by a fluid layer having a finite depth. The solution of the disk vibration problem is obtained using the boundary conditions at the free surface of the fluid layer and the boundary conditions at the fluid layer–poroelastic medium interface. The solution is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic impedance coefficient are examined based on different water depths, poroelastic materials, disk permeabilities and frequencies of excitation. Based on the numerical results, it is proposed that the hydrodynamic pressure caused by the foundation vibration is the intrinsic reason that the existence of a fluid layer has such a great effect on the dynamic characteristics of the foundation. In many cases, the hydrodynamic pressure caused by the foundation vibration cannot be ignored when designing dynamic underwater foundations. These results are helpful in understanding the dynamic response of foundations under still water without water waves, such as foundations in pools, lakes and reservoirs. 相似文献
17.
Jeng-Tzong Chen Jia-Wei Lee Chine-Feng Wu I-Lin Chen 《Soil Dynamics and Earthquake Engineering》2011,31(5-6):729-736
Following the success of seismic analysis of a canyon [1], the problem of SH-wave diffraction by a semi-circular hill is revisited using the null-field boundary integral equation method (BIEM). To fully utilize the analytical property in the null-field boundary integral equation approach in conjunction with degenerate kernels for solving the semi-circular hill scattering problem, the problem is decomposed into two regions to produce circular boundaries using the technique of taking free body. One is the half-plane problem containing a semi-circular boundary. This semi-infinite problem is imbedded in an infinite plane with an artificial full circular boundary such that degenerate kernel can be fully applied. The other is an interior problem bounded by a circular boundary. The degenerate kernel in the polar coordinates for two subdomains is utilized for the closed-form fundamental solution. The semi-analytical formulation along with matching boundary conditions yields six constraint equations. Instead of finding admissible wave expansion bases, our null-field BIEM approach in conjunction with degenerate kernels have five features over the conventional BIEM/BEM: (1) free from calculating principal values, (2) exponential convergence, (3) elimination of boundary-layer effect, (4) meshless and (5) well-posed system. All the numerical results are comparing well with the available results in the literature. It is interesting to find that a focusing phenomenon is also observed in this study. 相似文献
18.
Roland Klees 《Surveys in Geophysics》1993,14(4-5):419-432
The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m2 digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km2 with an accuracy of the order 10–3 to 10–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques. 相似文献
19.
Adrian Costea Quoc T. Le Gia Ernst P. Stephan Thanh Tran 《Studia Geophysica et Geodaetica》2011,55(3):465-477
We consider the exterior Neumann problem of the Laplacian with boundary condition on spheroids. We propose to use spherical
radial basis functions in the solution of the boundary integral equation arising from the Dirichlet-to-Neumann map. Our meshless
approach with radial basis functions is particularly suitable for handling scattered satellite data. We also propose a preconditioning
technique based on an overlapping domain decomposition method to deal with ill-conditioned matrices arising from the approximation
problem. 相似文献
20.
PETER FURNESS 《Geophysical Prospecting》1993,41(6):779-790
Two methods for computing spontaneous mineralization potentials in the region external to the source body are reviewed. The first of these is a long-established technique in which the causation is assumed to be a distribution of simple current source on the boundary of the mineralization. The second is a more recent technique which assumes a surface distribution of current dipole moment (double layer) along the boundary of the source body. The former technique is a special case of a more general spontaneous potential (SP) model in which the source is a density of current dipole moment (current polarization) distributed throughout the mineralization. As far as the potentials in the region external to the source body are concerned this current polarization can be simply related to an equivalent double layer source function, i.e. the potential discontinuity produced over the boundary of the mineralization by an equivalent double layer model. This simple relationship suggests an integral equation technique for the exact numerical solution of boundary value problems appropriate to the polarization model for spontaneous mineralization potentials. The technique is applied to exploring the justification of interpreting mineralization self-potentials by the traditional approach. 相似文献