IBEM for Impedance Functions of an Embedded Strip Foundation in a Multi-Layered Transversely Isotropic Half-Space

An indirect boundary element method (IBEM) is developed to study the dynamic impedance functions (stiffness coefficients) of a rigid strip foundation embedded in a multi-layered viscoelastic transversely isotropic (TI) half-space. The proposed IBEM using half-space Green's functions of distributed loads as fundamental solutions have the merits of fictitious loads being directly applied on the real boundaries without the problem of singularity and of the discretization effort restricted to local boundaries. In addition, the accuracy of the proposed method is not affected by the thickness of the discrete TI layers, as the exact dynamic stiffness matrix is employed. The presented algorithm is verified via comparisons with published results for the isotropic medium. By taking a rigid strip foundation embedded in a homogeneous half-space, a single-layered half-space, and a multi-layered half-space as examples, the effects of material anisotropy, frequency of excitation, and soil layer on the impedance functions are studied in detail. Numerical results show that impedance functions for the TI medium can be significantly different from those of the isotropic case. The variation of TI parameters alters the dynamic characteristics of the TI layered site, which in turn alters the dynamic interaction between the soil and foundation. In addition, the soil sedimentary sequence also has a remarkable influence on the impedance functions.