Symmetrized splitting operator method for dynamic consolidation problem of saturated porous semi-infinite foundation

Abstract The u-p form of dynamic consolidation equation provides a convenient approach to get insights into lots of low frequency practical engineering problems. Since the coupling of the dynamic consolidation equation, the existing numerical methods are generally full-implicit or staggered implicit which are always time-consuming. As a motivation to give a fast numerical algorithm for multi-field coupling problems, we construct a symmetrized splitting method in this paper to solve the u-p dynamic consolidation equations and lead to a second-order explicit scheme. To eliminate the reflection of the artificial boundary waves, we have derived the flow conditions of the artificial visco-spring boundary (VSB) for semi-infinite 3D saturated foundations, and presented principle for virtual displacements of the dynamic consolidation problem with artificial VSBs. Furthermore, we take the VSB condition of the fluid-solid two-phase saturated medium into consideration, to simulate the dynamic response process of saturated porous semi-infinite foundation system. The high computational efficiency and stability of the proposed method are verified by the numerical experiments.