饱和层状地基的薄层法基本解及其旁轴边界  

Basic solution of saturated layered ground by thin layered method and its paraxial boundary

作　　者：时刚[1,2] 高广运[2] 冯世进[2] 

机构地区：[1]郑州大学土木工程学院,河南郑州450001 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《岩土工程学报》2010年第5期664-671,共8页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(50878155;50678128)

摘　　要：在Biot饱和多孔介质理论的基础上,应用Fourier级数展开和Hankel变换方法,将Biot波动方程转化为一组二阶常微分方程;运用薄层法在竖向进行离散求解,最终得到层状饱和地基Lamb问题的解答。针对薄层法仅能在有限深度内求解的不足,根据旁轴近似原理,对饱和半空间频率–波数域内的刚度矩阵进行二阶Taylor级数展开,得到适合于薄层法底层边界的通用旁轴近似解答,提高了薄层法的计算效率。最后,通过两个计算实例验证了本文解答。The dynamic response of saturated layered ground subjected to harmonic force is investigated.By using the Fourier series expansion and Hankel transform,the Biot’s dynamic equations in each layer are reduced into a series of ordinary differential equations,which can be solved by the thin layered method（TLM）.And the general solutions for displacement and pore pressure in frequency domain are derived by analytical inversion of the Hankel transform.In order to overcome the problem that TLM only can work in finite depth,a solution of paraxial approxination,which can act as the underlayer boundary of TLM,is obtained by using the Taylor’s series expansion with respect to the stiffness matrix of saturated half-space soil in wave-number domain.Finally,two examples are presented to validate the proposed method.

关 键 词：饱和层状地基 GREEN函数 薄层法 旁轴边界 

分 类 号：TU470[建筑科学—结构工程]