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.
出处
《岩土工程学报》
EI
CAS
CSCD
北大核心
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)
关键词
饱和层状地基
GREEN函数
薄层法
旁轴边界
saturated layered half-space
Green’s function
thin layered method
paraxial boundary
