Study On The Analytical Method Of The Scattering Of Plane Waves By Conyons In Saturated Half Space

Our country which located in intersection area of the world's two major seismic belt is a country with frequent earthquakes.With the increase of population and the shortage of land resources in our country,more and more construction objects are built on the complex local irregular topography conditions.At present,research on seismic response for local site effect is mainly based on the single-phase medium.However,most of the earth's surface layer is saturated medium,and the seismic response analysis of the local site in the saturated two-phase media is still very few.Therefore,the study of the influence of local site on the seismic response of saturated two-phase media is a very meaningful and valuable subject.Canyons is a typical local irregular topography.Many scholars have studied the seismic response with the example of the Canyons.At present,most of the analytical solutions for the dynamic response of the local site are mostly obtained by the'Assumption of large arc' in two phase saturated media.Therefore,it can be seen that the analytical solution obtained by the 'Assumption of large arc' is an approximate solution.Many scholars have obtained some results through the indirect boundary element method,but the boundary element method is a numerical method.Sometimes it is difficult to meet the actual demand on the precision and boundary.In this paper,based on Biot saturated two-phase medium wave theory,the Mixed solution method of Hankel function integral transformation and the Fourier-Bessel series expansion are used to solve the boundary condition of horizontal surface.This kind of analytical method avoid the 'Assumption of large arc' to study Canyons plane wave scattering in two phase saturated medium and get some conclusions.the research results are as follows:1.Using the Mixed solution method of Hankel function integral transformation and the Fourier-Bessel series expansion,the analytical solution of the conyon in saturated two-phase medium under incidence of P and SV waves are respectively obtained.2.The solution in this paper can be degraded to single phase,compared with previous results are calculated by using of a 'Assumption of large arc',analyz effective and applicable condition of the method in this paper.Calculated In the condition of saturated Phase approaching free field and stress boundary indicate the analytical solution obtained in this paper is accurace Accurate and meet the precision requirement.The results are compared with those calculated by the 'Assumption of large arc' under the condition of saturated two-phase,show the method in the treatment of the canyon topography on seismic wave scattering problems have certain advantages.3.The influence of the incident frequency,incident angle and the porosity of saturated porous media on the seismic response of the conyons is analyzed by MATLAB.The results show that:(1)When the conyons exists,the change of the displacement amplitude is more complex when the incident wave frequency increases.(2)The displacement amplitude decreases with the increase of the incident angle.(3)when the incident wave is perpendicular to the incident,the displacement amplitude is symmetrical.When the incident wave oblique incidence,the left displacement amplitude is more complex than the right side of the conyons,and the left displacement amplitude is larger.(4)The porosity increases,the horizontal displacement amplitude decreases,and the vertical displacement amplitude is not obvious.(5)The displacement amplitude is approximately the same compare with the two boundary conditions,but the displacement amplitude is larger under the undrained boundary condition.