Study On Theory Of Elastic Half-Space For Soil-Foundation Dynamic Interaction

Soil-structure dynamic interaction is the dynamic responding of soils, foundation and superstructures excited by wave propagation in soils and structure virtually and, dynamic analysis of soil-foundation interaction is the key problem in studying soil-structure interaction. In the dissertation, based on a generalized shear-beam model, for homogeneous stratified foundations and non-homogeneous stratified foundations with exponential/power function shear modulus, random seismic responses of these foundations /the beams on these foundations are studied respectively. And mostly, lead/dynamic interaction characters of elastic half-space ground and rectangular plate/the beam are evaluated respectively.In the dissertation, first, based on a generalized shear-beam model, for homogeneous stratified foundations and non-homogeneous stratified foundations with exponential /power function shear modulus, closed-form analytical expressions are derived for natural frequencies, modal displacements, participation factors and steady state response function. And the orthogonal property of the modal displacements is proved, and then, dynamic responses of these foundations to earthquake are studied by the theory of random vibration. Two cases of power spectral intensity function for the earthquake acceleration input at the base rock are considered: the white noise spectrum and filter white noise spectrum. Afterwards, thinking soil-structure interaction, for shear-beams on homogeneous stratified foundations and non-homogeneous stratified foundations with exponential/ power function shear modulus, natural frequencies, seismic characteristic and random seismic responses of the beams are studied respectively.Secondly, in rectangular coordinate, integral representations for displacements of elastic half-space ground subjected to arbitrary vertical dead load are obtained by double Fourier integral transform method. Based on the integral representations for displacements of elastic half-space ground subjected to arbitrary vertical dead load and the analytic solution of an elastic rectangle plate with four free edges or the analytic solution of an elastic beam with two free ends, the analytic solutions of both an elastic rectangle plate with four free edges and an elasticbeam with two free ends rested on an elastic half space ground are given by the Fourier expanding respectively, including distribution disciplinarians for deflections, contact pressures and internal forces of the plate /the beam. Furthermore,Numerical results show the relations between these distribution disciplinarians and some physics parameters, geometrical sizes of the plate / the beam and the ground.Based on the analytic solution of an elastic rectangle plate with four free edges rested on an elastic half space foundation, for the first time, it analyses the magnitude relationship between foundation's horizontal displacement and foundation's vertical displacement, the distribution regularity about foundation's horizontal displacement and vertical displacement along the foundation depth, simulation functions, simulation parameters. By the foundation displacements distribution regularity along the foundation depth, a three—parameters refined foundation model is brought forward to consider foundation's horizontal displacement. At the same time, by numerical calculation method, it verifies all sorts of approximate boundary conditions of an elastic rectangle plate with four free edges rested on double—parameters foundation and the calculation accuracy about better similar boundary conditions of an elastic rectangle plate with four free edges rested on double—parameters foundation.Thirdly, the work is extended to the case of arbitrary vertical harmonic load on elastic rectangular thin plate with four free edges / elastic beam with two free ends rested on elastic half-space ground. On the analogy of this, the solutions for 3-D dynamic responding of elastic rectangular thin plate/the elastic beam rested on elastic half-space ground subjected to arbitrary vertical harmonic loading are presented Based on an integral representation for displacements of elastic half-space ground subjected to arbitrary vertical harmonic load. Finally, the numerical analysis for dynamic interaction characters of elastic half-space ground and rectangular plate/the beam are evaluated respectively.