Dynamic Response of Arbitrarily Shaped Foundation Embedded in Multilayered Partially Saturated Half-Space

A novel precise flexibility matrix algorithm is proposed to analyze the dynamic response of a rigid foundation embedded in a multilayered partially saturated half-space (MLPSH) that consists of several dry soil layers and saturated soil layers overlying on a saturated half-space. The wave equations of dry soil layers and saturated soil layers governed by Biot's theory are transformed into a dual vector form. The extended precise integration algorithm is applied to combine microlayers between two interfaces of any two typical layers. Subsequently, the global flexible matrix is assembled based on relative positions of source and receiver points. Finally, the dynamic impedance of the embedded foundation is achieved by using the flexible volume method. The accuracy and effectiveness of the proposed method are validated by comparing them with the results of extended studies. Extensive numerical results are presented to investigate the influence of the foundation shape on the dynamic impedance of the foundation embedded in an MLPSH.