Dynamic impedance functions of rigid strip foundation on a multi-layered transversely isotropic half-space
Ba Zhenning1,2 Hu Liming1 Liang Jianwen1,2
1. Department of Civil Engineering, Tianjin University, Tianjin 300072, China;
2. Key Laboratory of Coast Civil Structure Safety of the Ministry of Education, Tianjin University, Tianjin 300072, China
Abstract：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 wave number 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 foundations resting on the half-space with the normal sedimentary sequence. The dynamic impedance functions of the half-space with the inverted sedimentary sequence fluctuate violently with the frequency and the values are relatively large.
