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.