层状横观各向同性地基中埋置刚性基础的平面外动力刚度系数

采用间接边界元方法(IBEM)求解了层状横观各向同性(TI)地基中埋置刚性基础的平面外动力刚度系数。首先将层状TI地基与埋置刚性基础的交界面采用线边界单元离散,然后求解层状TI半空间中斜线均布荷载动力格林影响函数,最后由刚性基础与层状TI地基确立的混合边界条件求得动力刚度系数。通过与各向同性地基中基础动力刚度系数的比较验证了方法的正确性,进而以均质TI地基、单一TI土层地基和多TI土层地基中埋置刚性基础模型为例进行了数值计算分析,讨论了土体的TI性质对动力刚度系数的影响。研究表明层状TI地基与均质TI地基中埋置基础的动力刚度系数有着本质的差异;单一TI土层地基中基础动力刚度系数的峰值频率由TI土层的竖向剪切模量决定,而峰值则由水平剪切模量决定;多TI土层地基中基础的动力刚度系数与其等效单一TI土层地基中基础的动力刚度系数亦有着显著的差异,且这种差异又与土层的排列次序有关。

Anti-plane dynamic stiffness coefficient of a rigid foundation embedded in a multi-layered TI ground

The anti-plane dynamic stiffness coefficient of a rigid foundation embedded in a multi-layered transversely isotropic (TI) ground is obtained by using the indirect boundary element method (IBEM). Firstly, the interface of the rigid foundation is discretized into line boundary elements. Then, the dynamic Green’s functions for uniformly distributed loads acting on an inclined line are solved. Finally, the dynamic stiffness coefficient of the rigid foundation is determined through the mixed boundary conditions between the foundation and the layered TI foundation. The accuracy of the method is verified by comparing results with the dynamic stiffness coefficients of rigid foundation embedded in an isotropic foundation. The rigid foundations embedded in a uniform TI foundation, in a single TI layer foundation and also in a multi-layered TI foundation are numerically calculated, and the effects of TI parameters on the dynamic stiffness coefficient are studied. The numerical results show that the dynamic stiffness coefficient in the layered TI foundation is significantly different from that in the uniform TI foundation. For the single layered TI foundation, the peak frequency of the dynamic stiffness coefficient is determined by the shear modulus in the vertical direction, while the peak value is determined by the shear modulus in the horizontal direction. The dynamic stiffness coefficient of the multi-layered foundation is obviously different form that of the single layered TI foundation, and these differences are in turn related to the ordering of the TI layers.