Research On Semi-Analytical Element Method For Dynamic Problems Of Unsaturated Elastic Half-Space Foundation

The dynamic problem of unsaturated elastic half-space foundations has always been widely concerned by the academic and engineering circles.It involves many disciplines such as mechanics,mathematics,and geotechnical engineering.It has academic value for the development of elastic mechanics and for the development of construction engineering and road engineering.Wide application value.In the past,most researches focused on the isotropic elastic foundation model and saturated soil foundation model.However,unsaturated soils are more common in practical engineering,so the steady-state response of the elastic half-space of unsaturated soils is unavoidable.Moreover,the semi-analytical method combines the advantages of the numerical method and the analytical method,and simplifies the cumbersome degree of calculation.With the increase of the number of semi-analytical function terms,the conclusions obtained better meet the requirements.Based on the semi-analytical method,this paper establishes a theoretical system for solving the dynamic problems of unsaturated elastic half-space foundations.The dynamic characteristics of unsaturated elastic foundations are analyzed by numerical calculation using Matlab software self-programming.The specific contents are as follows:(1)This paper derives the dynamic control equation of unsaturated porous media based on the unsaturated soil and the basic equations of seepage proposed by the predecessors,clarifies the physical meaning of each parameter,and establishes the mechanical model and boundary of the unsaturated elastic half-space foundation Conditions,the free vibration of the unsaturated half-space foundation and the steady-state response governing equations of the unsaturated elastic half-space foundation are derived.(2)The semi-analytical element method is used to study the free vibration of the unsaturated elastic half-space foundation.Based on the free vibration dynamic control equation of the unsaturated soil and the boundary conditions of the unsaturated elastic half-space,select the appropriate displacement mode,establish the semi-analytical function of the foundation unit,and apply the weighted residual method to obtain the dynamic response of the unsaturated elastic half-space foundation Semi-analytical equation to analyze its natural frequency and natural vibration characteristics.(3)Using the governing equation of the unsaturated half-space foundation under harmonic load,the semi-analytical element method is used to study,and the weighted residual method is used to obtain the semi-analytical equation of the steady-state response of the unsaturated elastic half-space foundation,and the unsaturated elasticity is established The semi-analytical theory of the steady-state response of half-space foundations.(4)Using Matlab software to compile a program,numerically calculate the horizontal displacement and vertical displacement amplitude of the unsaturated foundation under vertical steady-state load,and numerically analyze the effects of saturation,foundation depth,frequency and other parameters on pore pressure and deflection.The impact of amplitude.The method in this paper is used to study the free vibration and steady-state response of the unsaturated elastic half-space foundation,and a feasible method to study the dynamic characteristics of the complex medium foundation is obtained.