层状横观各向同性地基上刚性条形基础动力刚度系数  

Dynamic impedance functions of rigid strip foundation on a multi-layered transversely isotropic half-space

作　　者：巴振宁[1,2] 胡黎明[1] 梁建文[1,2] 

机构地区：[1]天津大学土木工程系,天津300072 [2]天津大学滨海土木工程结构与新材料教育部重点实验室,天津300072

出　　处：《土木工程学报》2017年第9期67-81,共15页China Civil Engineering Journal

基　　金：国家自然科学基金(51578373;51578372)

摘　　要：采用间接边界元方法(IBEM)研究了层状横观各向同性(TI)地基上明置条形基础平面内动力刚度系数。首先,在波数域中求解TI介质动力平衡方程,建立了TI土层和TI半空间的精确动力刚度矩阵,并通过集整土层和半空间刚度矩阵,求得层状TI地基整体动力刚度矩阵。然后,采用刚度矩阵方法求得层状TI地基表面均布荷载动力格林函数。最后,由基础与地基表面的混合边界条件求得明置条形基础的平面内动力刚度系数。均布荷载动力格林函数的引入克服了传统边界元方法的奇异性问题,同时,精确动力刚度矩阵的引入使得方法不受土层厚度的限制。通过与已有结果比较验证了方法的正确性,并以均匀TI半空间地基、单一TI土层地基和多TI土层地基上明置基础为例进行了数值计算分析,探讨了TI参数、振动频率和土层对刚度系数的影响。研究表明,土体TI参数对刚度系数有着显著的影响,尤其是层状TI地基中刚度系数的峰值频率和峰值十分依赖于TI参数的变化;逆序地基与正常序列地基上基础刚度系数差异明显,逆序地基对应刚度系数随频率振荡剧烈且数值较大。An indirect boundary element method （IBEM） is used to study the in-plane dynamic impedance functions （or dynamic-stiffness coefficients） of a strip foundation on multi-layered transversely isotropic （TI） half-space. First, the dynamic equilibrium equations for the TI media are solved in the wavenumber domains, and the exact dynamic stiffness matrices for the TI layer and the TI half-space are established. The global matrix is then formulated by assembling the matrices of all the layers and of the half-space. Second, Green＇ s functions are derived for the layered TI media with uniformly distributed loads acting on its surface. Finally, formulations of the dynamic impedance functions are presented by introducing the mixed boundary conditions for the interface between the foundation and the ground surface. By introducing the Green＇ s functions of distributed loads into the IBEM, the problem of singularity associated with the classical boundary integral equation method （BIEM） can be overcome. Additionally, due to the utilization of exact dynamic stiffness matrices, the new method is not affected by the thickness of the discrete TI layers. The IBEM algorithm is verified by comparing with the published results, and then it is utilized to study the dynamic impedance functions of a rigid strip foundation resting on a uniform TI half-space, a single layered TI half-space, and a multi-layered TI half-space, respectively. The effects of material anisotropy, frequency of excitation and soil layers on the dynamic impedance functions are studied in detail. Numerical results show that the TI parameters have important impacts on the dynamic-stiffness coefficient. In particular, the peak frequencies and peak values of the dynamic impedance functions for the foundation resting on layered TI half-space are heavily dependent on TI parameters. The dynamic-stiffness coefficients of the foundations resting on the half-space with the inverted sedimentary sequence are significantly different from those of the foundati

关 键 词：动力刚度系数 横观各向同性 层状地基 条形基础 间接边界元法 

分 类 号：TU470[建筑科学—结构工程]