Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach
Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach
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DOI：
10.1016/j.soildyn.2007.04.001
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发表时间：
2008
影响因子：
4
通讯作者：
Jeng-Tzong Chen;Pocheng Chen;Chia-Tsung Chen
中科院分区：
文献类型：
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作者：
Jeng-Tzong Chen;Pocheng Chen;Chia-Tsung Chen
本文在零场积分方程中采用退化核和傅里叶级数展开，求解了含冲积河谷的Helmholtz外问题。在积分方程中使用退化核的主要优点是通过将零场点精确地定位在真实的边界上而无需计算奇异积分的主值。针对极坐标系中圆形边界的退化核特性，提出了一种自适应观测器系统。半平面问题采用镜像概念和分解技术。将零场点移至真实的边界，匹配边界条件，得到一个线性代数系统，无需边界离散。代数系统中的未知系数可以很容易地确定。由于误差只归因于傅里叶级数的截断，因此本方法被视为“半解析”解。SH波入射时冲积河谷或峡谷场地的地震反应分析是主要关注的问题。算例包括单个和连续的冲积河谷，以测试我们的程序。一个单一的峡谷和两个连续的峡谷的限制情况下也得到解决。在本研究中还观察到了软盆地的扩大。验证了半解析方法的有效性。我们的优点，适定的模式，主值自由，消除边界层效应和指数收敛和无网格，使用本方法。
In this paper, the degenerate kernels and Fourier series expansions are adopted in the null-field integral equation to solve the exterior Helmholtz problems with alluvial valleys. The main gain of using degenerate kernels in integral equations is free of calculating the principal values for singular integrals by locating the null-field point exactly on the real boundary. An adaptive observer system is addressed to fully employ the property of degenerate kernels for circular boundaries in the polar coordinate. Image concept and technique of decomposition are utilized for half-plane problems. After moving the null-field point to the real boundary and matching the boundary conditions, a linear algebraic system is obtained without boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a “semi-analytical” solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples including single and successive alluvial valleys are given to test our program. Limiting cases of a single canyon and two successive canyons are also addressed. Amplification of soft basin is also observed in this study. The validity of the semi-analytical method is verified. Our advantages, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence and mesh-free, by using the present method are achieved.