Split Operator Method For 3D Dynamic Consolidation Equations Of Saturated Medium

Liquefaction instability often occurs in embankment dams and their foundations under strong earthquakes.In order to study the liquefaction instability of saturated embankmentdam and its foundation,the soil is often regarded as a two-phase medium material composed of pore water and soil skeleton,and the dynamic consolidation equation of this two-phase saturated medium is solved numerically.A finite element model for dynamic consolidation equation of embankment dam is needed.This numerical model is a system of interaction between a finite foundation and a dam structure,which is intercepted by semi-infinite foundation.The artificial boundary formed by the intercept finite foundation should reflect the wave radiation effect in the infinite medium of the saturated porous medium,that is,the artificial boundary condition.The artificial viscous-spring boundary of saturated porous media is more complex than that of a single solid medium.It is not only necessary to consider the boundary conditions of solid consolidation displacement,but also to consider the boundary conditions of pore water pressure.In this paper,the Strang splitting operator method for solving the dynamic consolidation equation of two phase saturated medium is set up,and the expression after introducing the artificial boundary is introduced,and the application source code program is developed.The dynamic response process of the saturated medium under different dynamic load is analyzed,and the absorption effect of the artificial viscous-spring boundary is verified and the effect of the artificial viscoelastic boundary is verified.Its validity and correctness.The specific research contents are as follows:1.The classical Strang splitting operator method is studied.The u-p form splitting scheme for governing equations of two phase saturated medium dynamic consolidation is given.And based on its weak solution form,the script file of finite element language is written.2?Based on Finite Element Program Generator(FEPG),a FORTRAN source codeprogram for solving the dynamic consolidation problem of 3D two-phase saturated medium is generated.3.The mathematical expression of analytic solution of spherical traveling wave and the stress,displacement and flow boundary conditions of the 3D saturated medium on artificial boundary are studied.The weak solutions of the Strang splitting operator method for the dynamic consolidation equation of the two-phase saturated medium with the artificial viscous-spring boundary are given.4.A finite element program for 3D dynamic consolidation of two-phase saturated medium with viscous-spring artificial boundary is developed.At the same time,the dynamic response under impact load,sudden load and different medium parameters is analyzed.And verify the stability and correctness of the Strang splitting algorithm for solving the governing equations and the viscous-spring artificial boundary program.The calculation results of dynamic response of 3D saturated medium show that the Strang explicit splitting operator method can be used to effectively solve the dynamic consolidation problem of two-phase saturated medium.The further introduction of the artificial viscous-spring boundary can more effectively simulate the propagation process of the near field wave and the radiation damping of the far field.