Analytical Analysis Of Free Site Seismic Ground Motion In Unsaturated Soil

Our country locates the world’s two major seismic zones.According to historical records, the earthquake happened almost all the provinces. As a boom of economy,a growing number of marvelous construction projects started emerging.In order to ensure the security of the construction project under the seismic action,the crucial issue of free field seismic response needs to be studied.The majority of present study focuses on the research that the field is simplified to single phase or two phases saturated state.However,in fact,most of the media we are living in the natural environment are unsaturated state,that is,the gas exists in the pore medium.Therefore,it is particularly important to analyze the free site seismic ground motion of three-phase unsaturated porous media.Firstly, in this paper we introduced the control equations of unsaturated porous medium under the conditions of several different linear elastic deformations. Among the equations the displacement vector of each phase was decomposed by Helmholtz, then using the Fourier transform to get the solution of the equations. It was shown that three longitudinal waves and one transverse wave existed in unsaturated porous media. We analyzed the effect of saturation on body waves under the condition of unsaturated sites with different elastic constants of porous media.Upon the basis of the fluctuation characteristics of unsaturated porous media, we established the unsaturated soil free field model and analyzed the wave field where the plane wave (P wave and SV wave) came. According to the site boundary conditions, we can obtain the undetermined coefficients. And then the analytical solution of unsaturated soil free site seismic ground motion would be gained in the case of P wave and SV wave incidence. On the basis of analytical solutions, we calculated and analyzed the effects of saturation, incident angle, incident wave frequency, soil rigidity etc. for unsaturated soil free site seismic ground motion then got the following conclusion:(1) Under the condition of different relative frequency, the change of saturation has a significant effect on amplitude ratio and displacement amplification factor with the increase of the incident angle;(2) The free space in the non-saturation has the same resonance frequency, changes when it reaches saturation;(3)Under the condition of different soil stiffness, as the decrease of the soil stiffness the influence on amplitude ratio and displacement amplification factor gradually increase;(4)Under the condition of different soil porosity, as the increase of the soil porosity the influence on displacement amplification factor gradually increase;(5)Different soil depth there are differences in the impact on amplitude ratio and displacement amplification factor with the change of the saturation.(6)When the thickness of the unsaturated soil tends to infinity, the displacement is changed by the change of incident Angle. Among four different body waves the speed and attenuation of P1wave and S wave propagation are slower, so it is mainly considered the P1wave and S wave reflection and transmission characteristics in this paper. It can be realized that the existence of pore gas phase makes a dramatic difference on different body wave propagation characteristics in the unsaturated free space.In this paper, we present the analytic solution of unsaturated soil free site seismic ground motion in the case of P wave and SV wave incidence and get the universal rules and conclusions about unsaturated soil free field earthquake ground motions. The study will provide a reasonable explanation about complex seismic ground motion and provide technical support on complex local site area of large-scale structural seismic design.