沉积河谷-建筑群地震动力相互作用的二维IBEM模拟

众多城市坐落于沉积河谷之中,沉积河谷-密集建筑群间的地震动力相互作用规律尚不明确。采用间接边界元方法(IBEM),对在平面SV波入射下,沉积河谷-建筑群之间的地震相互作用进行二维模拟计算和参数分析。研究结果表明:沉积河谷-建筑群间存在着显著而复杂的地震动力相互作用;较浅沉积河谷中建筑群地震响应呈现强弱交替变换特征;入射波角度、沉积河谷的材料、几何特征是影响沉积河谷-建筑群整体地震响应规律的关键因素。总体上看,建筑群对浅沉积河谷地震动响应有较大的降幅效应,特别是高频波入射下最大降幅近50%。实际河谷地震放大效应评估需考虑密集建筑群的影响,而位于地震波聚焦位置的建筑物需适当提高设防标准。

平面SV波入射下地上建筑群-地铁隧道群动力相互作用研究

该研究采用一种高精度间接边界元方法(indirect boundary element method, IBEM),研究了平面SV波入射下地上建筑群-地铁隧道群的动力相互作用问题。研究表明:“建筑群-隧道群”系统存在显著的动力相互作用,其规律与入射波性质、建筑物和隧道数量排布等因素密切相关。通过对比不同建筑物数量对隧道动力响应的影响,能够发现:低频波作用下,建筑物对下穿隧道的动力响应有放大作用,而高频波作用下则会削弱隧道的动力响应,最多可以降低37.5%左右。从频域分析中可以看出:隧道对地震波有较强的屏蔽作用,从而降低了其上建筑群的地震响应。建筑群的存在降低了各个单体建筑的动力响应,但在高频波作用时位于建筑群来波一侧的建筑会产生较大的动力响应。该研究成果可为城市建筑群-地铁隧道群的动力相互作用分析以及地上建筑和地铁隧道的抗震设计提供理论依据。

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

The indirect boundary element method （IBEM） is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and effi- ciently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Scattering of seismic waves by three-dimensional large-scale hill topography simulated by a fast parallel IBEM

To solve seismic wave scattering by a large-scale three-dimensional(3-D) hill topography, a fast parallel indirect boundary element method(IBEM) is developed by proposing a new construction method for the wave field, modifying the generalized minimum residual(GMRES) algorithm and constructing an Open MP plus MPI parallel model. The validations of accuracy and efficiency show that this method can solve 3-D seismic response of a large-scale hill topography for broadband waves, and overcome the weakness of large storage and low efficiency of the traditional IBEM. Based on this new algorithm architecture, taking the broadband scattering of plane SV waves by a large-scale Gaussian-shaped hill of thousands-meters height as an example, the influence of several important parameters is investigated, including the incident frequency, the incident angle and the height-width and length-width ratio of the hill. The numerical results illustrate that the amplification effect on the ground motion by a near-hemispherical hill is more significant than the narrow hill. For low-frequency waves, the scattering effect of the higher hill is more pronounced, and there is only a single peak near the top of the hill. However, for high-frequency waves, rapid spatial variation of displacement amplitude appears on the hill surface.

3D-FSM·DDM IBEM numerical system of multi-medium

Based on the idea of the developed 3D-FSM.DDM boundary element method, the field with muti-medium was formulized firstly, then connected at the interface of two fields according to the continuous conditions of stress and displacement, after that, a boundary value problem with unified model was formed and solved. Ultimately, an applied numerical simulation system was developed. It was compared with the model having analytical solution for verifying the applicability and the calculating precision.

三维沉积盆地对地震动的放大效应——间接边界元法模拟

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.

用边界元法计算永磁体磁场

本文提出用间接边界元法计算任意界面的永久磁铁所产生的空间磁场，推导出其磁场计算公式。实际计算了稀土永久磁铁的磁场分布，并与实测值进行了比较。实际计算结果表明这是一种简单而实用的方法。

地基动力特性对地铁列车振动荷载诱发振动的影响

结合"分区契合"技术,采用间接边界元方法研究了地铁列车振动诱发的层状地基振动问题。方法首先将模型划分为含隧道的层状半空间和轨道下垫层两个区域。然后求解振动荷载作用于垫层表面时轨道下垫层区的自由波场,同时在两个区域的边界上分别施加单位虚拟荷载来模拟两个区域内的散射波场。最后契合两个区域,由边界条件求得虚拟荷载的幅值,进而求得地基的动力响应。文中进行了数值计算,着重分析了土层厚度、基岩与土层刚度比等地基动力特性参数对地表振动的影响,同时针对天津一典型地基和其等效单层土地基进行了比较研究,得出了一些有益的结论。

任意多个凸起地形对平面P波的散射

结合"分区契合"技术,采用间接边界元方法研究了任意多个凸起地形对平面P波的散射问题。求解中将模型分解为开口层状半空间域和多个凸起闭合域,同时将波场分解为自由波场和散射波场。自由波场由直接刚度法求得,而开口域和闭合域内的散射波场则通过在相应的边界上施加虚拟均布荷载,求解动力格林函数来模拟,虚拟荷载密度通过引入边界条件确定。该文通过与已有结果的比较验证了方法的正确性,进而开展数值计算,研究了两侧凸起高度、凸起间距和凸起个数对中间凸起及附近地表位移幅值的影响。数值结果表明:凸起间存在动力相互作用,使得多个凸起情况位移幅值显著大于单一凸起情况,多个凸起与单一凸起对应的位移幅值及放大谱均存在显著差异;两侧凸起的高度和凸起间距的改变,均使得凸起间动力相互作用机制发生了改变,进而改变了放大谱的峰值以及峰值频率。凸起个数对凸起间动力相互作用机制影响较小,不同凸起个数情况对应的放大谱峰值频率非常接近;两侧凸起高度的增大、凸起间距的减小以及凸起个数的增多,会使得凸起间动力相互作用进一步加强,位移幅值较大且空间分布更为复杂。

非连续屏障对Rayleigh波宽频散射三维快速边界元模拟

基于单层位势理论,将快速多极子-间接边界元方法(FMM-IBEM)拓展到弹性半空间群桩对弹性波的宽频散射求解,进而研究了Rayleigh波入射下多排桩屏障体系的隔振效果。数值试验表明该方法能够大幅度降低常规IBEM计算所需的存储量和计算量。针对典型算例,讨论了单排桩净距、排桩桩长、场地波速、排桩排数及多排桩之间净距对Rayleigh波的屏障效应。结果分析表明:排桩排数是影响多排桩隔振效果的主要因素,而多排桩之间的排距对隔振效果影响较小;桩间净距和桩长是影响单排桩隔振效果的重要参数,桩距在0.1倍~0.3倍Rayleigh波波长,桩长大于1倍波长时即可取得较好的隔振效果;对于不同的场地,场地土越软,排桩隔振效果越好。对低频波隔振宜采用多排桩进行隔振。

层状场地中任意形状沉积河谷对平面SH波的散射

利用间接边界元方法在频域内求解了层状场地中任意形状沉积河谷对平面SH波的散射;利用土层的精确动力刚度矩阵求解了应力和位移的动力Green函数;结合间接边界元法,研究了沉积河谷宽度、厚度、入射角、入射频率等对地表位移幅值的影响,并与按一维场地模型计算的结果进行了比较。研究表明,沉积河谷有明显的二维散射效应,与一维模型的计算结果差别显著。在工程场地地震安全性评价中,应合理考虑沉积河谷对场地设计地震动参数确定的影响。

层状场地中二维沉积谷地对弹性波的三维散射

为研究层状场地中二维沉积谷地对斜入射弹性波的三维散射问题,建立了求解问题的移动间接边界元方法。方法通过沿二维沉积谷地轴线方向的傅里叶变换将三维问题降为二维问题,进而在沉积谷地截面内进行边界单元的离散和求解,求得截面内的三维动力响应,然后将截面内的计算结果沿沉积谷地轴线方向进行波数展开即可求得任意位置动力响应。文中通过与前人结果的比较验证了方法的正确性,并以均匀半空间场地和基岩上单一土层场地为例进行了数值计算和分析,给出了一些有益的结论。

层状半空间中多层沉积谷地时域地震响应分析

基于作者此前提出的多域间接边界元方法,对多层沉积谷地的二维时域地震响应问题进行了研究。该方法在频域内求解,经由快速傅里叶逆变换叠加频域结果求得时域解答。采用全空间荷载格林函数和半空间格林函数分别构造沉积层闭合域内和开口半无限空间域内散射波场,使得两种格林函数的优势充分发挥。该研究验证了提出方法的正确性,进而以El Centro波作为输入地震动,进行了典型成层谷地的计算分析,重点讨论沉积层序对谷地附近地震动峰值和反应频谱的影响。研究表明,不同沉积层序情况对应的地表地震动时程及其地震反应谱有着显著差异,具体表现为沉积正常排列时,沉积内部水平加速度时程峰值最大,而对应的反应谱峰值周期最小;沉积层逆序排列时,沉积内部水平加速度时程峰值最小,而对应的反应谱峰值周期最大。另外,逆序沉积削弱了一部分中、高频波段的能量,相比正常沉积层序,起到了一定的“隔震”效果。

含滑移界面复合式衬砌隧道地震响应边界元模拟

采用一种高精度间接边界元方法(IBEM),求解了平面P、SV波入射下"围岩-减震层-浅埋衬砌隧道"体系地震响应及动应力集中效应。引入接触-滑移界面模型,模拟复合式隧道衬砌与围岩之间接触状态。结果表明:总体上看,随着界面滑移刚度因子增大,衬砌内壁动应力集中因子(DSCF)增大,无滑移状态下应力放大更为显著;SV波入射下,衬砌外壁DSCF则随滑移刚度因子增大而减小;P波垂直入射下,低频情况在隧道左右两端动应力集中十分显著,高频时则在隧道下部应力更为集中。另外,减震层的存在可有效降低衬砌动应力集中效应,随着入射频率增加,减震效果越好,隧道衬砌受力更为均匀;适当降低减震层弹性模量和加大减震层厚度,可取得更好的减震效果。

横观各向同性饱和沉积谷地对平面qP1波的散射

基于Biot流体饱和多孔介质模型,采用间接边界元方法(IBEM)在频域内求解了横观各向同性(TI)饱和沉积谷地对平面qP1波的散射问题。通过与各向同性饱和结果的对比验证了方法的正确性,开展了不同情况的数值计算分析,重点研究了沉积TI性质对地表动力响应的影响。结果表明:沉积TI性质对地表位移的幅值及其空间分布均有显著影响,且影响程度与qP1波的入射角度、入射频率和观测点位置有关。考虑沉积的TI性质可更为精确地模拟沉积谷地对平面qP1波的散射。

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.

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

Amplification of in-plane seismic ground motion by group cavities in layered half-space (Ⅱ): with saturated poroelastic soil layers

As the continuation study on amplification of in-plane seismic ground motion by underground group cavities in layered half-space, this study extends to the case of poroelastic half-space with dry poroelastic and saturated poroelastic soil layers. The influence of poroelastic layers on the amplification of seismic ground motion is studied both in frequency domain and time domain using indirect boundary element method （IBEM）. It is shown that for the example of a saturated poroelastic site in Tianjin under the excitation of Taft wave and E1 Centro wave, the amplification of seismic ground motion in poroelastic case is slightly smaller than that in the elastic case, and the amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum）.. can be increased up to 38.8% and 64.6%; the predominant period of response spectra in poroelastic case becomes shorter to some extent compared with that in the elastic case. It is suggested that the effect of underground group cavities in poroelastic half-space on design seismic ground motion should be considered.

Amplification of in-plane seismic ground motion by group cavities in layered half-space (Ⅰ)

Amplification of in-plane seismic ground motion by underground group cavities in layered half-space is studied both in frequency domain and time domain by using indirect boundary element method （IBEM）, and the effect of cavity interval and spectrum of incident waves on the amplification are studied by numerical examples. It is shown that there may be large interaction between cavities, and group cavities with certain intervals may have significant amplification to seismic ground motion. The amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum） can be increased up to 45.2% and 84.4%, for an example site in Tianjin, under the excitation of Taft wave and E1 Centro wave; and group cavities may also affect the spectra of the seismic ground motion. It is suggested that the effect of underground group cavities on design seismic ground motion should be considered.

3D Diffraction of obliquely incident SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space

Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.