基于切比雪夫谱元模型的成层场地地震反应分析  

Seismic response analysis of horizontal layered soil sites based on Chebyshev spectral element model

作　　者：邢浩洁 李鸿晶[1] 杨笑梅[2] XING Hao-jie LI Hong-jing YANG Xiao-mei(College of Civil Engineering, Nanjing Tech University, Nanjing, Jiangsu 211816, China College of Civil Engineering and Transportation, Guangdong University of Technology, Guangzhou, Guangdong 510006, China)

机构地区：[1]南京工业大学土木工程学院,江苏南京211816 [2]广东工业大学土木与交通学院,广东广州510006

出　　处：《岩土力学》2017年第2期593-600,609,共9页Rock and Soil Mechanics

基　　金：国家自然科学基金资助项目(No.51278245);supported by the National Natural Science Foundation of China(51278245)

摘　　要：将切比雪夫谱元模型应用于成层场地的一维波动分析,发展了一种具有高阶数值格式的场地地震反应时域分析方法。通过谱单元离散基岩和覆盖土体,建立各个单元的波动方程,并在基岩内设置透射人工边界,模拟底部无限域对内域波动的影响;利用切比雪夫正交多项式构造高阶单元位移模式,得到空间离散后的场地节点运动方程;利用中心差分原理,结合人工边界的数值格式,推导了一种稳定的时域积分数值方案。最后通过2个算例阐释了该方法在场地地震反应分析中的应用,并与传统方法进行了对比分析。数值试验表明,该方法具有高精度特性,在使用较少节点的条件下仍能得到较为可靠的计算结果,可显著地提高场地地震反应分析的计算效率。Chebyshev spectral element model is applied to one-dimensional wave propagation analysis of horizontal layered soil. A time-domain analysis is developed with high-order numerical scheme for the simulation of seismic response of soil site. The bedrock and upper soil are discretized by spectral elements, and the wave motion equation is applied to the domain of each element. Simultaneously, transmitting artificial boundary condition is introduced in the bedrock to simulate the influence of bottom infinite district on the interior wave motion. The Chebyshev orthogonal polynomials are used for constructing the displacement mode of the high-order elements, then a spatial discretization procedure is accomplished and the motion equation of all the computation nodes is obtained. A stable time-domain integration scheme is derived using the central difference theory and the numerical formulae of artificial boundary. Two soil sites seismic response problems are solved to compare the results using traditional methods. The proposed method provides remarkably enhanced computation efficiency for site seismic response analysis with high accuracy on small quantity of computing nodes.

关 键 词：场地地震反应 时域分析方法 切比雪夫谱元模型 高阶数值格式 一维波动 

分 类 号：TU435[建筑科学—岩土工程]