Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green＇s functions of compressive and shear wave sources are derived based on Biot＇s theory. The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verification of the accuracy is performed by： （1） checking the satisfaction extent of the boundary conditions, （2） comparing the degenerated solutions of a single-phased case with well- known solutions, and （3） examining the numerical stability of the solutions. The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.

Effects of a covering layer in a circular-arc canyon on incident plane SV waves

An analytical solution for scattering of incident plane SV waves by a circular-arc canyon with a covering layer was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of the covering layer on incident plane SV waves. It was shown that the covering layer in a canyon, even if it is very thin, amplifies incident plane SV waves tremendously, and the amplification can be two and half times more than that for a simple canyon; the stiffness and thickness of the covering layer also have great effects on incident plane SV waves.

Broadband Analytical Solution to the Scattering of Plane SV Waves by Circular Cylindrical Canyons

Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.

SV波斜入射时不同水体模拟方法下超高水头船闸地震反应分析

基于黏弹性人工边界的地震动斜入射方法模拟平面SV波不同角度入射情况,分别采用声固耦合法和附加质量法模拟闸室内水体,研究超高水头船闸闸室位移、应力和塑性损伤等地震反应,对比两种水体模拟方法计算结果的异同。结果表明:(1)整体上,两种方法计算得出的左、右闸墙地震反应结果随入射角度变化的规律基本一致;左闸墙受拉损伤的最大值均出现在入射角15°时,右闸墙受拉损伤的最大值均出现在入射角35°时;地震波入射角度对超高水头船闸动力响应影响较大,设计时应考虑地震波斜入射的影响。(2)当入射角较大时,采用声固耦合法计算的闸墙相对位移极值、主应力极值和受拉损伤结果偏保守的概率更大,对超高水头船闸结构设计来说更为安全。(3)建议两种计算方法相互参考和校核,推荐采用偏安全的结果进行超高水头船闸结构设计。

A series solution for surface motion amplification due to underground twin tunnels:incident SV waves

A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method.The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion.It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.

空沟对弹性波散射的时域分析:平面SV波入射

基于土‑结构相互作用理论,利用比例边界有限元法,将含有空沟地形条件的场地分解为近场系统和无穷远场系统。利用四叉树对近场计算区域进行网格精细化离散,并利用位移单位‑脉冲响应矩阵来表示近场和远场交界面上的相互作用力,从而将斜入射的平面SV波转化为作用在近场系统边界上的等效节点力来模拟入射波对近场系统的激励作用,建立了时域‑空间域弹性波传播问题的数值模型,通过数值算例验证了方法的有效性,分析了入射角和空沟深度等参数对隔振效果的影响。结果表明:隔振效果随着入射角的增大而增大;当入射角较大时,通过进一步增大空沟深度,可使得空沟发挥出更优的隔振效果。

多空沟对弹性波的散射及隔振性能分析:平面P-SV波入射

在地基振动控制中,较浅的单空沟由于散射效率低,隔振效果并不理想,而多空沟可以通过提高散射效率而达到理想的隔振效果。根据弹性动力学基本理论,在复数域上进行波函数展开,由空沟周边应力自由边界条件,并借助保角映射理论和多极坐标变换技术建立了问题的控制方程,给出了多空沟对平面P‑SV波散射的解析解答。以双空沟为例,参数分析了激励频率、空沟长度和空沟间距等因素对隔振效果的影响规律。结果表明:双空沟的隔振效果明显优于单空沟,并且随着空沟长度增加,隔振效果越好;存在一定的空沟间距使双空沟能发挥出更好的隔振效果。

单排空心管桩屏障对平面SV波的隔离效果研究

参考圆柱坐标系下一排圆柱体对弹性波的多重散射,根据桩土界面处应力和位移连续的条件,得到了非连续空心管桩屏障对入射平面SV波散射系数的理论解。通过引入无量纲位移幅值,即屏障后土体的竖向位移与入射平面SV波引起的竖向位移的比值,比较了不同形式的屏障对入射平面SV波的隔离效果。讨论了桩间距、屏障的位置和管桩的剪切模量(刚度)对单排空心管桩屏障对平面SV波隔离效果的影响,为非连续屏障的隔振设计提供了理论依据。

圆弧形沉积河谷场地在平面SV波入射下的动力响应

利用Fourier-Bessel级数展开法在频域内给出了圆弧形沉积河谷场地在平面SV波入射下动力响应的一个解析解,并分析了河谷宽度、河谷深度、入射波长和入射角度等因素对动力响应的影响。

弹性半空间中衬砌洞室对平面P波和SV波的散射(Ⅱ)——数值结果

采用一种高精度的间接边界积分方程法,给出了弹性半空间中衬砌洞室对入射平面P波和SV波散射的数值结果;同时通过参数分析,探索了入射波特性和衬砌特性对平面波散射的影响规律。计算结果表明:衬砌洞室附近波的散射与无衬砌情况相比差异显著;动力反应特征主要依赖于波入射角、入射波无量纲频率、衬砌内外材料刚度比等参数;P波和SV波入射下洞室附近地面运动的放大效应均十分明显;低频波入射下,刚性衬砌表面的动应力集中现象最为显著。

平面SV波入射下弹性半空间中三维球形洞室的动力响应

采用一种间接边界积分方程法求解了平面SV波入射下弹性半空间中三维洞室的动力响应问题。通过与已有结果的比较,验证了方法的计算精度。在此基础上,以半空间中圆球形洞室为例,对地表位移响应和洞周动应力集中特征进行了详尽的参数分析,并与二维模型进行了比较。研究表明:二维和三维模型对平面波的动力响应在平面内存在一定的相似性,但在波型转换上存在显著差别,尤其体现在响应峰值及空间分布特征上,并且随着频率的升高,空间分布差异愈加明显;在出平面方向,三维洞室周围存在着显著的波散射效应,而二维模型难以描述这种出平面波型转换现象。

圆弧形凹陷地形表面覆盖层对入射平面SV波的影响

利用 Fourier- Bessel级数展开法 ,给出了表面具有覆盖层的圆弧形凹陷地形对入射平面 SV波散射问题的一个解析解 ,并利用该解分析了不同深宽比凹陷地形表面覆盖层刚度和厚度对入射 SV波的影响 .结果表明 ,凹陷地形表面覆盖层的存在 ,即使厚度很薄 ,也会显著增加对入射 SV波的放大作用 ,该放大作用可达到单一凹陷地形的 2 .5倍以上 .覆盖层刚度和厚度的变化对入射平面

饱和土沉积谷场地对平面SV波的散射问题的解析解

把波函数展开方法用于饱和多孔介质中波的传播的研究中 ,给出了不同土层界面条件 (透水条件和不透水条件 )下具有饱和土沉积层的圆弧形沉积河谷场地对平面SV波散射问题的解析解 .其中沉积谷软土场地用饱和多孔介质的Biot动力学理论模拟 ,半空间场地用单相介质弹性动力理论模拟 .对于入射角大于临界入射角时 ,产生的面波的波函数用有限Fourier级数展开 ,这种方法适用于较大的入射波频率范围 ,这是现存的数值方法所不能比拟的一大优点 .文中算例分析了入射波频率和入射角对地震地面运动的影响 .

SV波入射下多重散射问题的改进算法以及双排非连续刚性屏障的隔振研究

相比起Aviles等学者的单排非连续刚性屏障隔振理论,采用更为完整的Fourier-Bessel函数系的级数展开表达式来研究弹性波的多重散射问题,结合位移连续的边界条件,并引入更具一般意义上的Graf加法定理,推导了无限均匀介质中任意分布的多个刚性圆柱体对于平面SV波入射时散射系数的理论解析解。随后,取所有的圆柱体位于相平行的两条直线上,则问题演变成为双排刚性桩屏障对于平面SV波的隔离问题。重点讨论了两排桩之间的间距h对屏障整体隔振效果的影响及其他的一些隔振性状。特别地,当h=0时,该问题退化为常见的单排非连续屏障的隔振问题。

弹性半空间中衬砌洞室对平面P波和SV波的散射(Ⅰ)——方法

采用一种高精度的间接边界积分方程法,求解了弹性半空间中任意形状衬砌洞室对入射平面P波和SV波的散射问题。在衬砌内外表面附近引入虚拟波源面,由该面上的柱面膨胀波源和剪切波源构造衬砌内外的散射波场,继而由边界条件建立方程并求解得到虚拟波源密度,总波场可由散射场和自由场的叠加而得。通过精度验证和稳定性检验,表明该方法具有极高的数值精度和数值稳定性。

平面SV波入射下半圆凸起地形地表运动解析解

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.

圆弧形层状沉积谷地对入射平面SV波散射解析解

利用Fourier-Bessel级数展开法给出了圆弧形层状沉积谷地对入射平面SV波散射问题的一个解析解,并分析了谷中层状沉积排列顺序及相对刚度等因素对散射的影响。

饱和土半空间中地下圆形衬砌洞室对平面SV波的散射

在Biot饱和多孔介质动力学理论的基础上,利用Fourier-Bessel级数展开法,通过对含有衬砌洞室的局部场地进行波场分析,得到饱和土半空间中圆柱形衬砌洞室对平面SV波的散射问题的解析解。经验证,本文得到的解可以退化为半空间单相介质的情况。通过与已有的单相弹性介质半空间中圆柱形衬砌洞室对平面SV波散射问题的解析解的对比,验证了此解的正确性。在解析解的基础上,数值计算给出洞口动应力集中放大系数,分析了入射频率和孔洞埋深对柱面上的应力集中因子的影响。