横观各向同性层状地基动应力响应的求解与分析  

Solution and analysis of dynamic stress response for transversely isotropic multilayered soil

作　　者：韩泽军[1] 林皋 周小文[1] 杨林青[3] HAN Ze-jun;LIN Gao;ZHOU Xiao-wen;YANG Lin-qing(School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong 510641, China;Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China;School of Civil Engineering, Tianhe College of Guangdong Polytechnic Normal University, Guangzhou, Guangdong 510540, Chin)

机构地区：[1]华南理工大学土木与交通学院,广东广州510641 [2]大连理工大学建设工程学部,辽宁大连116024 [3]广东技术师范学院天河学院建筑工程学院,广东广州510540

出　　处：《岩土力学》2018年第6期2287-2294,共8页Rock and Soil Mechanics

基　　金：国家自然科学基金青年科学基金项目(No.51508203);博士后科学基金面上资助(No.2015M570713);博士后科学基金特别资助(No.2016T90783)~~

摘　　要：动力响应问题的求解对于地基在外荷载作用下引起的弹性波动问题研究有重要的意义。本文提出了一种求解横观各向同性层状地基在施加时间简谐荷载作用下任意点的应力响应的算法。此算法利用傅里叶变换将广义平面应变问题频率-空间域的动力方程转化到频率-波数域内,结合对偶变量的引入,利用高精度的精细积分算法对状态方程进行求解,在得到频率-波数域内的位移响应的基础上,利用傅里叶逆变换得到任意点的动应力响应。简谐荷载不仅可以施加在地基表面,而且可以施加在地基内部。对比算例验证了本文算法的准确性,同时对地基各向异性特性、激励频率和阻尼比对动应力响应的影响进行了参数分析,为工程实际提供可靠的数值依据。The dynamic response is significant to the elastic wave problem in soil caused by the external load. This paper proposes a solution to calculate dynamic stress responses of an arbitrary point in a transverse isotropic multilayered soil subjected to a time-harmonic load. The generalized plane-strain equation is transformed from frequency-spatial domain into frequency-wave number domain by Fourier transformation in this algorithm. Combined with the introduction of the dual vector, the state equation is solved by the precise integration method. Based on the displacement response of the soil in the frequency-wave number domain, the dynamic stress response of any point is obtained by the inverse Fourier transformation. The time-harmonic load can be applied at the surface of the soil or under ground. The accuracy of the algorithm in this paper is verified by a comparison with an existing solution. An extensive parametric analysis on the influence of anisotropy, excited frequency and damping ratio on the dynamic stress response provides reliable numerical basis for engineering practice.

关 键 词：横观各向同性 层状地基 简谐荷载 动应力响应 精细积分算法 

分 类 号：O302[理学—力学]