Study On The Interaction Between Elastic Half Space Foundation And Stepped Rectangular Foundation Slab

Nowadays,has been widely used in practical engineering.However,most of the research work mainly concentrated in the situation of load acted on foundation plate with equal cross section,while the study of load acted on the were relatively less,especially the analytical solution of this problem was almost blank.Comprehensive consideration of the theoretical feasibility and engineering application,this paper mainly studied the stepped rectangular foundation slab on elastic half-space subgrade.Research ideas of this paper is considering the upper overhang and lower part of the stepped rectangular foundation slab as two rectangular plates with different sizes,which is short for upper plate and lower plate,respectively.According to engineering application,the stepped rectangular foundation slab is divided into three cases: the upper and lower plates are both thin,the upper part is thick and the lower plate is thin,the upper and lower part are both thick.Based on thin-thick plate theory,combining the governing equation of bending problem of upper and lower plate with control equation of lower plate bending problem and deformation compatibility equation between lower plate and foundation which is built through static analytical solution of elastic half-space subgrade,at the same time,using the same deflection in the same area of the upper plate and lower plate to obtain the coordination equation.Besides,boundary value problem of four sides free of orthotropic stepped rectangular foundation slab on elastic half-space foundation could be got through boundary and corner conditions of the two plates,which would be solved by double Fourier series with supplementary terms,and then obtain the static analytical solution.Using the elastic half-space foundation's integral transformation solution of dynamic steady state displacement when subjected to arbitrary vertical harmonic load in Cartesian coordinates,the analytical solution of steady-state vibration of four sides free of orthotropic stepped rectangular foundation slab on elastic half-space foundation could be got.This method avoid the drawbacks of numerical methods,abandon the previous assumptions about the reaction of the ground,and finally get the more realistic distribution law of deformation,internal force and contact reaction of the plate.