共查询到20条相似文献，搜索用时 62 毫秒
1.
Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis. The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations. 相似文献
2.
Scattering of a plane harmonic P, SV, or Rayleigh wave by a corrugated elastic inclusion completely embedded in a two-dimensional isotropic half space is investigated by using a direct boundary integral equation method. The corrugated scatterer is generated by superimposing a random perturbation of arbitrary amplitude to a smooth elliptical shape. The probability density function for the randomly corrugated inclusions is assumed to be of uniform or normal types. The displacement fields are evaluated along the half-space surface for a range of impedance contrasts, frequencies, five incident waves for circular- and elliptic-based rough inclusions. Subsequently, the roughness factor is introduced in terms of the surface response for the rough and the corresponding smooth inclusions. The results clearly show that this factor strongly depends upon the impedance contrast of the materials, the basic inclusion geometry, the type of incident wave, and the frequency. The peak values of the roughness factor are observed for the near-grazing SV incidence. Furthermore, the impedance contrast of the materials has a non-uniform effect upon the surface motion. While the smallest roughness factor is consistently observed for the minimal impedance contrast the peak values of the same factor may take place for different non-minimal impedance contrasts. For the range of frequencies considered here, the type of the random interface corrugation (random-uniform vs. random-normal) has a minimal effect upon the roughness factor. 相似文献
3.
Scattering of elastic waves by three-dimensional canyons embedded within an elastic half-space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non-axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress-free boundary conditions at the half-space surface. The boundary conditions are imposed locally in the least-squares sense at several points on the surface of the canyon and the half-space. Through a comparative study the validity and limitations of two-dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three-dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two-dimensional models. These results emphasize the need for three-dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering. 相似文献
4.
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 总被引：1，自引：1，他引：0
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. 相似文献
5.
Three-dimensional scattering of seismic waves by a cylindrical alluvial valley embedded in a layered half-space is investigated by using the combination of the boundary integral representation and the finite element method. The surface displacements due to incident plane harmonic body waves (P, SV and SH) propagating at an arbitrary angle to the axis of the cylindrical valley are evaluated numerically for two semi-elliptical alluvial valleys. The presence of the layer is found to have a strong effect on the amplification of the surface displacements in some cases. The three-dimensional motion seems to be quite critical and may cause large amplification. The surface ground motion becomes significant when compared with corresponding free-field motion as the wavelengths become comparable to the characteristic length of the valley. The maximum amplification always occurs atop the valley. Numerical results show that the amplitude and the amplification pattern of the surface displacement strongly depend upon the frequency, the angle and the type of the incident waves. 相似文献
6.
Scattering of plane harmonic P, SV, or Rayleigh waves by a two-dimensional rough cavity completely embedded in an isotropic
elastic half-space is investigated by using a direct boundary integral equation method. The cavity’s roughness is assumed
to be in the form of periodic or random perturbations of arbitrary amplitude superimposed to a smooth elliptical shape. For
the randomly corrugated cavities the normal or the uniform probability distribution functions are assumed. Based on multiple
random cavity results, the corresponding average surface response is computed. These are compared with the corresponding periodically
corrugated and smooth cavity responses. The surface response is evaluated for different cavity shapes and incident waves and
for a range of frequencies. The surface motion results are used to determine the peak surface motion frequencies. They depend
strongly upon the basic inclusion shape (the principal axes) and the nature of the incident wave. Strong similarity in the
peak surface motion frequencies can be observed for the rough and smooth cavity models for both circular and elliptical shapes.
In order to quantify the importance of the cavity corrugation upon the surface motion, a roughness influence factor is defined
in terms of the rough and smooth cavity surface responses. This factor strongly depends upon the type of the incident wave,
the nature of the cavity corrugation, the basic cavity shape, and the frequency. The factor clearly shows the effect of the
cavity roughness upon the surface motion. 相似文献
7.
采用波函数展开法及边界离散的方法给出了任意断面形状的地下夹塞对平面SH波散射的半解析解; 利用蒙特卡罗方法随机模拟产生了30组夹塞断面样本, 通过对该样本在平面SH波入射下地表位移幅值的统计分析, 研究了夹塞断面形状随机性对平面SH波散射的影响. 结果表明, 夹塞断面形状随机性对平面SH波的散射具有重要影响. 以圆形夹塞为例, 当断面半径的变异系数为0.1时, 地表位移响应幅值变异系数可达0.71. 随着入射频率的升高, 变异系数逐渐增大; 随着夹塞刚度的降低, 变异系数逐渐增大; 随着夹塞埋深的增加, 变异系数逐渐减小. 相似文献
8.
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
9.
Introduction Scattering of incident waves by local topographies is one of the most attractive topics in the field of engineering seismology. They can be resolved by either a numerical method or an analyti-cal method. The numerical methods include finite difference method, finite element method, boundary element method, etc. The analytical method is the wave function expansion method. Al-though numerical methods can be used for arbitrary-shaped topographies, the analytical solutions are still … 相似文献
10.
采用波函数展开法,并借助辅助函数思想,给出了平面SV波入射下半圆凸起地形地表运动的一个解析解,并对解答的收敛性和截断计算精度进行了检验;最后通过若干算例分析了入射频率和入射角度以及凸起地形宽度对地表运动的影响. 数值结果表明,凸起地形对入射SV波具有显著的放大作用, 该放大作用可达自由场的4倍以上. 当入射频率较低时, 位移峰值多位于半空间地表; 而当入射频率较高时,位移峰值多位于凸起地形表面. 相似文献
11.
Scattering of elastic waves by an orthotropic basin of arbitrary shape embedded in a half-space is investigated for the sagittal plane motion using an indirect boundary integral equation approach. Steady-state results were obtained for incident plane harmonic pseudo P-, S-, and Rayleigh waves. Detailed convergence analysis of the method is presented. Green's functions are evaluated by using adaptive Newton–Cotes or Filon quadratures. Surface ground motion is presented for semicircular and semielliptical basins with different material properties and various angles of incidence. The results show that surface motion strongly depends upon nature of incident wave, geometry and material properties of the basin, and location of the observation point. Comparison with isotropic basin response demonstrates that anisotropy is very important in amplification of surface ground motion. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
12.
Foundation soil interaction is studied using an analytical two-dimensional model, for circular foundations embedded in a homogeneous elastic half-space and for incident plane P- and SV- and for surface Rayleigh waves. The scattered waves are expanded in complete series of cyclindrical wave functions. A detailed analysis is presented of the foundation response to unit amplitude incident waves as a function of the type of incident waves and angle of incidence, the depth of the embedment and the foundation mass per unit length.It is shown that free-field translations and point rotation approximate well the foundation input motion only for very long incident waves. For shorter incident waves, those in general overestimate the foundation input motion. Neglecting the rotation of the foundation input motion (which is usually done in practice) may eliminate a major contribution to the base excitation of buildings and may cause nonconservative estimates of the forces in these buildings. Incident waves appear as ‘longer’ to a shallow foundation than to a deeper foundation. Therefore, deeper foundations are more effective in reflecting and scattering the short incident waves. 相似文献
13.
Scattering of elastic waves by two dimensional multilayered dipping sediments of arbitrary shape embedded in an elastic half-sapce is investigated by using a bondary method. The displancement field is evaluated throughout the elastic media for both steady state and transient incident SH waves. The unknown scattered field is expressed in terms of wave functions which satisfy the equation of motion, traction-free boundary condition and appropariate radiation conditions. The transient response is constructed from the steady state solution by using the fast Fourier transform technique. The numerical results presented demonstrate that scattering of waves by subsurface irregularities may cause locally very large amplification of surface ground motion. The motion can be affected greatly by the scattered surface waves in the sediments. The results clearly indicate that the surface ground motion depends upon a number of parameters present in the problem, such as frequency and the angle of incidence of the incoming wave, impedance contrast between the layers and location of the observation point. 相似文献
14.
弹性层状半空间中凸起地形对入射平面SH波的放大作用 总被引：7，自引：0，他引：7
对Wolf理论进行拓展,使之可解决凸起地形对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中凸起地形对入射平面SH波的放大作用问题。本文模型的显著特点之一是考虑了层状半空间的动力特性以及层状半空间和凸起地形的阻尼;特点之二是计算精度高。文中以基岩上单一土层中半圆凸起地形对入射平面SH波的放大作用为例进行了数值计算分析。研究表明,基岩上单一土层中凸起地形对入射平面SH波放大作用和均匀半空间中凸起地形有着本质的差别;土层动力特性不仅影响凸起地形地表位移的幅值,还会影响地表位移的频谱;阻尼会显著降低凸起地形对高频波的放大作用。 相似文献
15.
Ernest Heymsfield 《地震工程与结构动力学》1999,28(12):1651-1667
The direct boundary integral equation technique is used to study in-plane surface amplification of in-plane seismic body waves for the case of an inhomogeneity in a bedrock half-space. In the studied soil configuration, a soil layer rests on a rock half-space which includes a rock inclusion. The rock inclusion considered is a semi-infinite horizontal rock layer in which its upper boundary borders the soil layer. Materials in the soil–rock configuration are considered viscoelastic except for the section of the rock half-space below the level of the rock inclusion which is considered elastic. A parametric study is performed to determine controlling factors for surface displacement due to in-plane body waves. The study investigates varying the stiffness and the thickness of the rock inclusion for a range of frequencies and wave incidence angles. Anti-plane waves for this type of soil-rock configuration have been addressed in a previous article by Heymsfield (Earthquake Engng. Struct. Dyn. 28 : 841–855 (1999)). Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
16.
A boundary integral formulation is presented and applied to model the ground motion on alluvial valleys under incident P, S and Rayleigh waves. It is based on integral representations for the diffracted and the refracted elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources' strengths should be obtained as an intermediate step. Boundary conditions lead to a system of integral equations for boundary sources. A discretization scheme based on the numerical and analytical integration of exact Green's functions for displacements and tractions is used. Various examples are given for two-dimensional problems of diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response and suggest approximations of practical interest. For shallow alluvial valleys the response and its resonant frequencies are controlled by a coupling mechanism that involves both the simple one-dimensional shear beam model and the propagation of surface waves. 相似文献
17.
Scattering of elastic waves by an orthotropic sedimentary basin is investigated for antiplane strain model using an indirect boundary integral equation approach. Both steady state and transient response were obtained for semicircular and semielliptical basins with different material properties. The results indicate that the basin geometry and the impedance contrast between the half-space and the basin have similar effects on the surface ground motion amplification as for the isotropic case. However, the material anisotropy may change significantly the fundamental resonant frequencies of the basin, resulting in different surface displacement amplification patterns. In addition, it was observed that the arrival time of the main disturbance on the surface strongly depends on material anisotropy for different angles of incidence. The results demonstrate that material anisotropy may be very important in explaining surface ground motion amplification for sedimentary basins. © 1998 John Wiley & Sons, Ltd. 相似文献
18.
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
19.
20.
In this paper we analyse the two-dimensional scattering and diffraction of plane SH waves by a semi-elliptical canyon. The exact series solution of the problem, for general angle of incidence of the plane SH waves, has been used to examine the dependence of surface amplifications inside and near the canyon. The nature of ground motion has been found to depend on two key parameters: (a) The angle of incidence. (b) The ratio of the canyon width to the wave length of incident SH waves. For short incident waves surface displacement amplitudes change rapidly from one point to another, while for the long waves and shallow canyons displacement amplitudes display only minor departure from the uniform half-space amplification of 2. For shallow canyons and long incident waves, the angle of incidence introduces only minor changes into the overall behaviour of surface amplitudes. For deep canyons and nearly grazing incidences, a prominent shadow zone is realized behind the canyon. 相似文献