基于快速边界元法的多体多域弹性波散射模拟及其应用研究

发布时间：2018-02-22 09:18

本文关键词： 夹杂群山体裂纹大规模弹性波散射快速多极间接边界元法　出处：《天津城建大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,地震频发,给人们的人身及财产安全造成了巨大损害,如何减少地震灾害带来的伤害成了人们关注的焦点。而局部场地作为影响地震动的三大要素之一,对地震波在近地表的反应有有着重大的影响。现实生活中,人为修建的地下隧道、地铁车站、桩基、采煤井道以及各类地下管线,天然形成的熔岩、溶洞或者灾害导致的山体裂纹、地下断层等都将影响地震波的传播,或使得地震作用放大,或缩小,但不同的局部场地类型则会出现不同的反应。国内外现有规范仅仅指出建筑物、构筑物等要尽量避开上述不均匀场地的定性规定,而并未做出具体规定。针对上述问题,本文在传统边界元法的基础上,引进快速多极算法,针对多体多域弹性波散射问题进行研究,以期实现局部不均匀场地地震动的定量分析。首先,实现了固体中数百万大规模多体多域弹性波散射的快速模拟,验证了所发展方法的计算精度及效率。其次,夹杂群数值结果表明:二维SH波水平入射下,夹杂群上方半空间表面位移放大效应更为显著。特别是低频段,部分区域位移幅值达到5.0。高频SH波垂直入射下,空洞群和软夹杂群表现出明显的屏障效应,而硬夹杂群上方半空间表面位移放大和缩减区域会交替出现。全空间中夹杂群对P、SV波的散射同单夹杂情况具有显著差别,总波场空间分布特征更为复杂。平面P波入射下,夹杂体对弹性波的散射效应随着入射波频率的增加而更加显著。对于ka=1.0,夹杂体内外波速比β_/β_0=1/3时,由于夹杂体相互间多次散射的相干效应,夹杂体表明位移幅值竟达到2.2。最后,针对含裂纹(群)的山体弹性波二散射问题,在计算精度及效率的验证的基础上,分析裂纹群的存在对山体表面位移的影响。平面P波垂直入射下,少量较大尺寸裂纹的存在对山体表面竖向位移总是起屏障作用。而含有大量小尺寸裂纹的山体表面最大竖向位移幅值相对无裂纹存在的山体情况增加约9.7%,说明了裂纹群的存在对山体表明竖向位移有较大影响。另外,值得注意的是,山体表面水平位移最大值总是表现为放大的现象。综上所述,本文针对大规模多体多域以及山体裂纹弹性波散射发展了适合相应问题的快速多极间接边界元法,为复杂场地地震动的定量分析提供了理论参考依据。
[Abstract]:In recent years, frequent earthquakes have caused great damage to people's personal and property safety. How to reduce the damage caused by earthquake disasters has become the focus of attention. In real life, man-made underground tunnels, subway stations, pile foundations, coal mining tunnels and various underground pipelines, naturally formed lava, have a significant impact on the response of seismic waves near the surface. Cracks in the mountains caused by caves or disasters, underground faults, etc., will affect the propagation of seismic waves, or cause the earthquake to be magnified or reduced. However, different types of local sites will react differently. The existing codes at home and abroad only point out that buildings and structures should avoid the qualitative provisions of the above uneven sites as far as possible, but do not make specific provisions. In this paper, based on the traditional boundary element method, a fast multipole algorithm is introduced to study the scattering problem of elastic waves in multi-body and multi-domain, in order to realize the quantitative analysis of local uneven ground motion. The fast simulation of millions of large scale multibody and multi-domain elastic wave scattering in solids is realized, and the accuracy and efficiency of the developed method are verified. Secondly, the numerical results of inclusion group show that the two-dimensional SH wave is incident horizontally. The amplification effect of surface displacement above the inclusion group is more remarkable, especially in the low frequency band, the displacement amplitude of some regions reaches 5.0. At the vertical incidence of high frequency SH wave, the cavity group and the soft inclusion group exhibit obvious barrier effect. On the other hand, the displacement amplification and reduction of the surface of the upper half space of the hard inclusions occur alternately. The scattering of the PSV waves by the inclusions in the whole space is obviously different from that in the case of single inclusions, and the spatial distribution of the total wave field is more complicated. Under the incident of plane P wave, the distribution of the total wave field is more complex. The scattering effect of inclusions on elastic waves is more significant with the increase of incident wave frequency. For Ka1. 0. 0. 0. 0 / 3 of the velocity ratio of internal and external waves of inclusions, because of the coherence effect of multiple scattering between inclusions, the displacement amplitude of inclusions is 2.2. Finally, when the velocity ratio of internal and external waves is 尾 / 尾 0 / 0 / 1 / 3, the displacement amplitude of inclusions can reach 2.2. Based on the verification of calculation accuracy and efficiency, the influence of the existence of crack group on the surface displacement of mountain body is analyzed. The existence of a small number of large size cracks always acts as a barrier to the vertical displacement of the mountain surface, while the maximum vertical displacement amplitude of the mountain surface with a large number of small cracks increases by about 9.7% compared with that of the mountain with no crack, indicating that the maximum vertical displacement amplitude of the mountain surface with a large number of small cracks increases by about 9.7%. The existence of crack group has great influence on the vertical displacement of mountain body. It is worth noting that the maximum horizontal displacement of the mountain surface is always shown as an amplification phenomenon. In summary, a fast multipole indirect boundary element method suitable for the corresponding problems is developed for the scattering of elastic waves from large scale multi-body and multi-body cracks. It provides a theoretical reference for quantitative analysis of ground motion in complex sites.
【学位授予单位】：天津城建大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P315.9

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