复杂三维沉积盆地对弹性波散射的快速边界元模拟及应用

发布时间：2018-03-21 18:16

本文选题：三维均质沉积盆地　切入点：三维层状沉积盆地　出处：《天津城建大学》2017年硕士论文　论文类型：学位论文

【摘要】：多次震害表明:不同场地条件下震害差异显著,而沉积盆地作为一种典型复杂场地,对地震波具有显著的放大作用。本文针对三维均质沉积盆地和三维层状沉积盆地对弹性波散射问题,采用离散单元少、精度高、自动满足无限远处边界条件的间接边界元方法(IBEM)进行了求解,并通过精度验证,验证了该方法的精度。但是,由于IBEM在求解虚拟荷载密度时,所形成的大矩阵为非对称稠密矩阵,故求解所需计算量和存储量巨大,无法有效计算大规模高频实际问题。为了提高计算速度,减少计算内存,本文引入了子结构并行算法,该算法在一定程度上提高了计算速度,减少了计算内存。但是采用该算法在计算大规模高频实际问题时,存储量仍然十分巨大,无法应用于大规模高频实际问题。所以本文引入了被誉为二十世纪十大算法之一的快速多极算法(FMM),FMM算法通过树结构,可将源点对场点的作用分类计算,然后迭代求解得到虚拟波源密度,而不需要求出和存储大矩阵,该方法极大的降低了求解问题所需的计算量和存储量,使该问题得到了妥善解决。目前,国内大多数学者对于沉积盆地弹性波散射问题的研究还局限于理论分析阶段,对于实际场地的分析较少,而在国外,许多学者已经将研究成果应用于实际场地中去,从而为实际工程建设、地震区划提供理论依据,因此,本文将快速多极间接边界元方法(FM-IBEM)应用于某三维复杂形状均质沉积盆地在SV波作用下的地震响应求解和三维非水平层状沉积盆地在P、SV波作用下的宽频带求解,得到了沉积盆地地表地震响应的若干规律,同时检验了本方法对各类复杂场地的适用性,计算结果也可为其他数值方法提供参考对照。研究结果表明:FM-IBEM作为一种新的高效算法和实用程序,适合于沉积盆地对弹性波散射问题的求解,可以极大地提高计算效率,有利于进一步将该算法应用于大规模高频实际问题的求解中去,从而为复杂场地条件下地震区划、城市地震危险性评估、城市规划及重大工程抗震设防提供重要理论依据和有力参考。
[Abstract]:The results of multiple earthquakes show that there are significant differences in earthquake damage under different site conditions, and sedimentary basin is a typical complex site. In this paper, the scattering of elastic waves by three-dimensional homogeneous sedimentary basins and three-dimensional stratified sedimentary basins is studied. The discrete elements are few and the accuracy is high. The indirect boundary element method (IBEM), which automatically satisfies the infinite boundary conditions, is solved, and the accuracy of the method is verified by accuracy verification. However, because IBEM is solving the virtual load density, The large matrix formed is asymmetric dense matrix, so the computation and storage required to solve the problem is too large to effectively calculate the large scale high-frequency practical problem. In order to improve the computing speed and reduce the computational memory, a substructure parallel algorithm is introduced. To a certain extent, the algorithm improves the computing speed and reduces the computational memory. However, when the algorithm is used to calculate large scale high-frequency practical problems, the storage capacity is still very large. This paper introduces a fast multipole algorithm known as one of the ten algorithms in the 20th century. By tree structure, we can classify and calculate the action of source point to field point. Then the virtual wave source density is obtained by iterative method without the need to calculate and store large matrices. This method greatly reduces the computational and storage requirements for solving the problem, and makes the problem well solved. The study of elastic wave scattering in sedimentary basins is still limited to the theoretical analysis stage, and the analysis of practical sites is less. In foreign countries, many scholars have applied the research results to the actual sites. So as to provide theoretical basis for practical engineering construction and seismic zoning, therefore, In this paper, the fast multipole indirect boundary element method (FM-IBEMEM) is applied to solve the seismic response of a three-dimensional homogeneous sedimentary basin with complex shape under SV waves and the broadband solution of 3-D non-horizontal stratified sedimentary basin under the action of PS-SV wave. Some laws of seismic response on the surface of sedimentary basins are obtained, and the applicability of this method to various complex sites is also tested. The results also provide a reference for other numerical methods. The results show that as a new and efficient algorithm and practical program, the solution to elastic wave scattering problem in sedimentary basins can greatly improve the computational efficiency. It is helpful to further apply this algorithm to the solution of large scale high-frequency practical problems, so that it can be used for seismic regionalization and urban seismic risk assessment under complex site conditions. Urban planning and seismic fortification of major projects provide important theoretical basis and powerful reference.
【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

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