Impedance functions of three-dimensional rectangular foundations embedded in multi-layered half-space

Although most of the building foundations are approximate to embedded three-dimensional rectangular foundations of different length-to-width ratios, the two-dimensional models or axis-symmetric models which ignore the influence of length-to-width ratios, are usually used for dynamic analysis due to less computational effort on impedance functions. The impedance functions of foundations characterized by different length-to-width ratios and depth-to-width ratios embedded in multi-layered half-space, are obtained by a boundary element method, combined with non-singular Green's functions of high efficiency. Results of high precision based on dense element meshing are presented on complete eight impedance functions (two horizontal, two coupled, two rocking, vertical and torsional impedance functions) for the practical values in the dynamic analysis of the buildings.