饱和半空间中凹陷地形对平面波散射解析方法的研究

发布时间：2018-01-03 21:45

本文关键词：饱和半空间中凹陷地形对平面波散射解析方法的研究　出处：《北京交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：我国处在世界两大地震带交汇处,是一个地震多发的国家。随着我国人口的增长和土地资源的紧缺,更多的工程项目将建设在地形复杂的局部地形上。目前,在局部场地对地震响应影响的研究上主要是采用单相介质进行讨论的。但地球表面土层很多情况是饱和介质,目前对饱和两相介质中的局部地形地震动力响应分析还比较少。所以研究饱和两相介质下局部地形对地震响应的影响是一项很有意义和价值的课题。凹陷地形是局部地形中一种比较有代表性的地形,很多学者研究局部地形的地震响应问题都是以凹陷地形为例。目前,很多在研究两相饱和介质中局部地形的动力响应解析解时,大部分是借助了“大圆弧假定”来处理半空间表面边界问题。故可把由“大圆弧假定”所求的解析解看作是一种近似解。也有很多学者通过间接边界元的方法得到了一些成果,但边界元法归根结底是一种数值的方法。在精度和边界上有时很难满足实际需求。本文以Biot饱和两相多孔介质波动理论为基础,利用Hankel函数积分变换和Fourier-Bessel级数展开混合求解的方法,处理水平地表边界条件,避开“大圆弧假定”,以此来研究饱和两相介质中凹陷地形对平面波散射的问题,并得到关于本文方法的一些结论,具体研究成果如下:1.采用Hankel函数积分变换和Fourier-Bessel级数展开混合求解的方法分别得到了平面P、SV波入射下饱和两相介质中凹陷地形在透水边界条件和不透水边界条件下的地震波散射的解析解。2.把本文得到的解退化到单相情况,与前人采用“大圆弧假定”的计算结果进行对比,分析了本文方法的有效性并得到本文方法的适用范围。通过在饱和两相情况下逼近自由场和应力边界条件计算,验证了本文方法的准确度和精度。另外在饱和两相情况下也和前人用“大圆弧假定”得到的结果作了对比,得到本文方法在处理凹陷地形对地震波散射问题时有一定的优势。3.采用MATLAB进行编程计算,分析了入射波频率、入射角和饱和多孔介质孔隙率对凹陷地形地震动力响应的影响。研究表明:(1)凹陷地形存在时,入射波频率的增加,位移幅值的变化越复杂。(2)入射角度的增加,位移幅值逐渐减小。(3)入射波垂直入射时,位移幅值成对称分布。入射波斜入射时,位移幅值在凹陷地形左侧变化较右侧复杂,且左侧位移幅值也较大。(4)孔隙率增大,水平向位移幅值减小,竖直向位移幅值变化不明显。(5)两种边界条件下的位移幅值变化规律大致相同,但不透水边界条件下的位移幅值较大。
[Abstract]:China is located at the intersection of two major seismic zones in the world and is a earthquake-prone country. With the growth of population and the shortage of land resources, more engineering projects will be built on local topography with complex terrain. The influence of local site on seismic response is mainly discussed by single-phase medium, but many of the earth's surface soil layer is saturated medium. At present, the analysis of local topographic dynamic response in saturated two-phase medium is relatively few. Therefore, it is a meaningful and valuable topic to study the influence of local topography on seismic response in saturated two-phase medium. A typical terrain in a local terrain. Many scholars have studied the seismic response of local topography as an example. At present, many researchers are studying the analytical solution of local topography in two-phase saturated medium. Most of them are based on the "big arc assumption" to deal with the surface boundary problems in half space. The analytical solution is regarded as an approximate solution, and many scholars have obtained some results by indirect boundary element method. However, the BEM is a numerical method in the final analysis. It is difficult to meet the practical requirements in terms of accuracy and boundary. This paper is based on the Biot saturated two-phase porous media wave theory. By using the method of Hankel function integral transformation and Fourier-Bessel series expansion, the boundary condition of horizontal surface is dealt with and the "big arc assumption" is avoided. In this paper, we study the scattering of plane waves by the depression topography in saturated two-phase medium, and get some conclusions about the method in this paper. The concrete research results are as follows: 1. The plane P is obtained by the method of Hankel function integral transformation and Fourier-Bessel series expansion. The analytical solution of seismic wave scattering in saturated two-phase medium under permeable boundary condition and impermeable boundary condition. 2. The solution obtained in this paper is reduced to the single-phase case. The results are compared with those calculated by the former "big arc assumption". The validity of the proposed method is analyzed and the applicable range of the proposed method is obtained. The method is calculated by approximating the free field and the stress boundary conditions under saturated two-phase conditions. The accuracy and accuracy of the proposed method are verified. In addition, the results obtained in the case of saturated two-phase are compared with the results obtained from the "large arc assumption". It is concluded that the method in this paper has some advantages in dealing with the scattering problem of seismic waves caused by depression topography. 3. The frequency of incident wave is analyzed by MATLAB programming. The influence of incident angle and porosity of saturated porous media on the seismic dynamic response of the depression topography. The study shows that the frequency of incident wave increases when the topography of the sag exists. The more complex the variation of displacement amplitude is, the more complex the incident angle is, the smaller the displacement amplitude is, the smaller the displacement amplitude is, when the incident wave is incident vertically, the displacement amplitude is symmetrically distributed, and the incident wave is oblique incident. The variation of displacement amplitude on the left side of the sag is more complicated than that on the right side, and the amplitude of displacement on the left side is larger than that on the right side, and the porosity increases and the amplitude of horizontal displacement decreases. The variation of vertical displacement amplitude is not obvious under two boundary conditions, but the displacement amplitude under impermeable boundary condition is larger.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU435

【相似文献】