Dynamic Response Analysis Of Saturated Soil Based On Singular Boundary Method

In recent years,as the rapid development of transportation system in China.People are pursuing better life to meet diverse requirements.In addition,automobiles,subways,and high-speed railways have become the main modes of transportation for people ’s usual travel and tourism activities.Thus,people’s travel frequency has been increasing,which has brought a heavy burden to the transportation system.Engineering problems such as uneven settlement,collapse,cracking,and long-term settlement of the road surface have occurred one after another,causing major casualties and serious economic losses,which has severely hindered the healthy development of the society.As a matter of fact,these severe engineering accidents are closely related to the dynamic response of saturated soil caused by various types of loads.It is of great significance to research the dynamic response of saturated soil under various types of loads.Nevertheless,the geometry and boundary conditions of practical engineering problems is non-trivial.The domain is usually semi-infinite or infinite.The boundary method is a better choice for the problems of this type.Owing to the singular boundary method(SBM)is mesh-free,simple to pre-processes and mathematically simple.In addition,the fundamental solutions used as the kernel functions makes the SBM extraordinarily available for semi-infinite and infinite problems.Therefore,in our thesis,a boundary-type meshless collocation method,the SBM is employed to solve the dynamic response problems of saturated soil under various types of loads.The main work of this paper is as follows:(1)Based on the Biot’s theory,the governing equations of dynamic response of saturated soil are obtained.The fundamental solutions of the dynamic response problem of saturated soil are derived via Helmholtz decomposition and matrix eigen-analysis.Then the origin intensity factors(OIFs)are derived for the SBM with different boundary conditions.(2)The SBM formulation is established based on the fundamental solutions of the dynamic response problem of saturated soil and the corresponding the OIFs.The accuracy and convergence of the SBM is presented via several numerical examples,including problems with square domain,half-space problems and twin-tunnel cases.(3)In practical engineering,the dynamic response problems of saturated soil is usually a transient problem.The SBM in conjunction with the exponential window method(SBM-EWM)are proposed to solve the transient problems.The exponential window method is an improved fast Fourier transform with the artificial damping.The accuracy and effectiveness of the SBM-EWM is verified with analytical solutions of square domain and the dynamic response of the single tunnel embedded in a saturated soil half-space at different times.