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1.
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
2.
3.
Transient response of three dimensional dipping layers of different shapes subjected to incident P, SV, SH and Rayleigh waves is investigated. The time domain response is constructed from steady state solutions through the Fourier synthesis. An indirect boundary integral equation method is applied to calculate the required steady state solutions. The material of the half-space and the layer is assumed to be linear, weakly inelastic, homogeneous and isotropic. Numerical results show that the maximum amplification of motion is strongly dependent upon the type of incident wave, the shape of the basin and signal frequency. The change in the shape of the valley from hemispherical to semi-prolate causes a significant increase in the amplitude of surface waves near the edges; however, the maximum amplification of motion near the centre of the valley decreases. This phenomenon is especially apparent for the case of an incident P wave. In comparison to the corresponding two dimensional responses, the amplitude of motion near the centre of the valley is in general higher for three dimensional models. 相似文献
4.
本文采用复变函数方法研究了稳态水平剪切波(SH波)在各向异性弹性半空间中任意形状孔洞上的散射及其对地面运动的影响.在变换空间中构造出自动满足各向异性半空间水平表面上应力为零的散射波函数,并根据孔洞表面应力为零的边界条件,采用最小二乘法求解散射波函数的系数.用介质的各向异性性质来模拟地质条件,给出了SH波作用下含圆孔、椭圆孔和方孔的各向异性半空间表面位移幅值的数值结果,并分析了介质特性、孔洞的形状、埋深、入射波波数及入射角度等因素对地面运动的影响规律.数值结果表明:介质的各向异性对含有孔洞的半空间表面的地表位移具有显著的影响;沿一定角度的入射波在某一频段内所引起的地表位移幅值比各向同性介质的可能要大,且随着孔洞埋深的增加,地表位移的幅值逐渐减小. 相似文献
5.
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
6.
Scattering of incident plane harmonic pseudo P‐, SH‐, and SV‐waves by a two‐dimensional basin of arbitrary shape is investigated by using an indirect boundary integral equation approach. The basin and surrounding half‐space are assumed to be generally anisotropic, homogeneous, linearly elastic solids. No material symmetries are assumed. The unknown scattered waves are expressed as linear combinations of full‐space time‐harmonic two‐dimensional Green functions. Using the Radon transform, the Green functions are obtained in the form of finite integrals over a unit circle. An algorithm for the accurate and efficient numerical evaluation of the Green functions is discussed. A detailed convergence and parametric analysis of the problem is presented. Excellent agreement is obtained with isotropic results available in the literature. Steady‐state surface ground motion is presented for semi‐circular basins with generally anisotropic material properties. The results show that surface motion strongly depends upon the material properties of the basin as well as the angle of incidence and frequency of the incident wave. Significant mode conversion can be observed for general triclinic materials which are not present in isotropic models. Comparison with an isotropic basin response demonstrates that anisotropy is very important for assessing the nature of surface motion atop basins. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
7.
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
8.
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
9.
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
10.
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
11.
柱面波在半空间中洞室周围的散射 总被引：2，自引：1，他引：1
采用一种间接边界积分方程法求解了柱面波在半空间中洞室周围的散射问题。通过边界条件的验算以及退化解答与精确解的比较,验证了本文方法的计算精度。文中主要分析了入射波频率、波源与洞室距离等参数对洞室附近地表位移响应和洞室动应力集中的影响,得出了一些有益的结论。 相似文献
12.
The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design. 相似文献
13.
Marijan Dravinski 《地震工程与结构动力学》2003,32(5):653-670
Scattering of plane harmonic waves by a three‐dimensional basin of arbitrary shape embedded within elastic half‐space is investigated by using an indirect boundary integral equation approach. The materials of the basin and the half‐space are assumed to be the most general anisotropic, homogeneous, linearly elastic solids without any material symmetry (i.e. triclinic). The unknown scattered waves are expressed in terms of three‐dimensional triclinic time harmonic full‐space Green's functions. The results have been tested by comparing the surface response of semi spherical isotropic and transversely isotropic basins for which the numerical solutions are available. Surface displacements are presented for a semicircular basin subjected to a vertical incident plane harmonic pseudo‐P‐, SV‐, or SH‐wave. These results are compared with the motion obtained for the corresponding equivalent isotropic models. The results show that presence of the basin may cause significant amplification of ground motion when compared to the free‐field displacements. The peak amplitude of the predominant component of surface motion is smaller for the anisotropic basin than for the corresponding isotropic one. Anisotropic response may be asymmetric even for symmetric geometry and incidence. Anisotropic surface displacement generally includes all three components of motion which may not be the case for the isotropic results. Furthermore, anisotropic response strongly depends upon the nature of the incident wave, degree of material anisotropy and the azimuthal orientation of the observation station. These results clearly demonstrate the importance of anisotropy in amplification of surface ground motion. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
14.
基于一种高精度间接边界元法(IBEM), 实现了沉积盆地三维地震响应的频域、 时域精细求解, 并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例, 着重探讨了入射角度、 入射波型、 入射频率、 盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律． 结果表明: 盆地形状对地震波的放大效应和空间分布状态具有显著影响, 且具体规律受控于入射波频段． ① 随着盆地深度增大, 盆地边缘面波发育更为充分, 在较宽频段内均会出现显著的地震动放大效应, 且深盆地的放大区域集中于盆地中部． ② 圆形盆地对地震波的汇聚效应最为显著, 而狭长盆地对地震波的汇聚作用相对较弱, 高频情况下可在盆地内部形成多个聚焦区域． ③ 不同波型入射下, 盆地对地震动放大效应的机制有所差异: P波入射下, 竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致; SV波入射下, 边缘面波汇聚效应相对较弱, 而当盆地较深时, 底部透射体波和边缘面波易形成同相干涉从而显著放大地震动． 按盆地内外介质波速比为1/2, P波和SV波垂直入射下频域最大放大倍数分别为25和15, 时域放大倍数约为4.0和3.7(雷克子波)． ④ 低频波入射下, 位移从盆地中部向边缘逐渐减小, 且浅层沉积盆地对地表位移幅值的放大作用不明显． ⑤ P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响． 相似文献
15.
Ismail Albayrak Vladimir Nikora Oliver Miler Matthew O’Hare 《Aquatic Sciences - Research Across Boundaries》2012,74(2):267-286
The effects of leaf shape, serration, roughness and flexural rigidity on drag force imposed by flowing water and its time
variability were experimentally studied in an open-channel flume at seven leaf Reynolds numbers ranging from 5 to 35 × 103. The study involved artificial leaves of the same surface area but with three shapes (‘elliptic’, ‘rectangular’ and ‘pinnate’),
three flexural rigidities, smooth-edge and sawtooth-like serration, and three combinations of surface roughness (two-side
rough, one-side rough/one-side smooth, and two-side smooth). Shape was the most important factor determining flow-leaf interactions,
with flexural rigidity, serration and surface roughness affecting the magnitude but not the direction of the effect on drag
control. The smooth-edge elliptic leaf had a better hydrodynamic shape as it experienced less drag force, with the rectangular
leaf showing slightly less efficiency. The pinnate leaf experienced higher drag force than the other leaves due to its complex
geometry. It is likely that flow separation from 12 leaflets of the pinnate leaf prevented leaf reconfiguration such as leaflets
folding and/or streamlining. Flexural rigidity strongly influenced the leaf reconfiguration and augmented the serration effect
since very rigid leaves showed a strong effect of serration. Furthermore, serration changed the turbulence pattern around
the leaves by increasing the turbulence intensity. Surface roughness was observed to enhance the drag force acting on the
leaf at high Reynolds numbers. The results also suggest that there are two distinctly different flow-leaf interaction regimes:
(I) regime of passive interaction at low turbulence levels when the drag statistics are completely controlled by the turbulence
statistics, and (II) regime of active interaction at high turbulence levels when the effect of leaf properties on the drag
statistics becomes comparable to the turbulence contribution. 相似文献
16.
The ground motion and wave propagation resulting from the scattering of anti-plane (SH) waves by a deep semi-elliptical hill on an elastic half-space are investigated. The solution is the closed-form one based on the method of wave-function expansion, and the expansion of elliptical sine and cosine over the half-range [−π/2, π/2]. The analysis shows that the interference of ground motion depends on several factors such as frequency of the incident waves, incident angle, and the aspect ratio of elliptical hills. Similar to part I: Shallow Hill, numerical results when semi-elliptical tends to semi-circular are compared with the work done by Lee et al. [17]. 相似文献
17.
The dynamic response of a finite number of flexible surface foundations subjected to harmonic incident Rayleigh or SH waves is presented. The foundations are assumed to be resting on an elastic half-space. The results show that the foundation stiffness has a marked effect on the vertical response, while there is only a minor effect on the horizontal displacements. In general, the dynamic response decreases with increasing foundation stiffness. In cases of Rayleigh wave incidence, the existence of an adjacent foundation generates a certain amount of horizontal response in the direction perpendicular to the incident wave and subsequently causes the system to undergo a torsional motion; while in cases of horizontally incident SH waves, a vertical response has been observed and its magnitude is comparable to the response in the direction of the incident wave. 相似文献
18.
Marijan Dravinski 《地震工程与结构动力学》1983,11(3):313-335
Scattering of plane harmonic SH, P, SV and Rayleigh waves by several inclusions of arbitrary shape, completely embedded into an elastic half-space, is considered. Perfect bonding between the half-space and the inclusions is assumed. The problem is investigated for linear, isotropic and homogeneous elastic materials. The displacement field is evaluated throughout the elastic medium so that the continuity conditions between the half-space and the inclusions are satisfied in mean-square sense. Numerical results of the surface displacement field are evaluated for single and two elliptic inclusions. The results show the following: (a) presence of a subsurface inhomogeneity may lead to large amplifications of the surface ground motion; (2) different surface displacement patterns emerge for different incident waves; (3) the presence of an additional inclusion may change significantly the surface displacement response of a single inclusion; (4) the surface motion extremes strongly depend upon (i) angle of incidence; (ii) frequency of incident field; (iii) embedment depth of the inclusions; (iv) separation distance between the inclusions; (v) material properties of the half-space and the inclusions; and (vi) location of observation point on the surface of the half-space. 相似文献
19.
To increase the safety and efficiency of tunnel constructions, online seismic exploration ahead of a tunnel has become a valuable tool. One recent successful forward looking approach is based on the excitation and registration of tunnel surface‐waves. For further development and for finding optimal acquisition geometries it is important to study the propagation characteristics of tunnel surface‐waves. 3D seismic finite difference modelling and analytic solutions of the wave equation in cylindrical coordinates reveal that at higher frequencies, i.e., if the tunnel‐diameter is significantly larger than the wavelength of surface‐waves, these surface‐waves can be regarded as Rayleigh‐waves confined to the tunnel wall and following helical paths along the tunnel axis. For lower frequencies, i.e., when the tunnel surface‐wavelength approaches the tunnel‐diameter, the propagation characteristics of these surface‐waves are similar to S‐waves. We define the surface‐wave wavelength‐to‐tunnel diameter ratio w to be a gauge for separating Rayleigh‐ from S‐wave excitation. For w > 1.2 tunnel surface‐waves behave like S‐waves, i.e. their velocity approaches the S‐wave velocity and the particle motion is linear and perpendicular to the ray direction. For w < 0.6 they behave like Rayleigh‐waves, i.e., their velocity approaches the Rayleigh‐wave velocity and they exhibit elliptical particle motion. For 0.6 < w < 1.2 a mixture of both types is observed. Field data from the Gotthard Base Tunnel (Switzerland) show both types of tunnel surface‐waves and S‐waves propagating along the tunnel. 相似文献
20.
Rayleigh’s method of approximation is employed to find out the reflection and transmission coefficients due to an incident
plane SH wave at a corrugated interface between a laterally and vertically inhomogeneous anisotropic elastic solid half-space
and a laterally and vertically inhomogeneous isotropic visco-elastic solid half-space. The lateral and vertical inhomogeneities
are described by the exponential variations of elastic parameters. The formulae of reflection and transmission coefficients
are derived in closed form for the first-order approximation of the corrugation. The effects of the corrugation of the interface,
the inhomogeneity, the anisotropy, the visco-elasticity and the frequency of the incident wave on these coefficients are studied
analytically and numerically for a specific model containing a periodic interface. The results of earlier workers have been
reduced as particular cases from the present formulation. 相似文献