Theoretical Solutions Of Spatially Variable Seismic Motions In Circular-arc Two-phase Layered Saturated Site Under Surface Water

China is located in the Asia-Europe earthquake zone,the Indian Ocean seismic zone and the Pacific Rim seismic zone.It is an earthquake-prone country with a land area of 9.6 million square kilometers and a coastline of more than 18,000 kilometers.Chinese water area is more than 4.7 million square meters.Therefore,it is necessary to study the impact of site factors on earthquake motion.With the national strategic and the engineering technology development,these reaserches can ensure the safety of those huge and complicated structures constructed at sea in the event of major earthquake disasters.In the aspect of the seismic response study,the difference in earthquake motion input will greatly affect the structural seismic response.At the same time,the rationality of earthquake motion input depends on the characteristics of the topography and geology of the structure,which constrains the seismic analysis results of the structure.The existing researches have great impetus and limitations on the seismic response analysis.They can not fully reflect the actual environmental effects of the structure.In order to provide more scientific and reasonable earthquake motion input,the scattering of incident plane P waves in complex terrain is studied by using the wave function expansion method in this paper.The terrain has comprehensive feature attributes such as a overlying layer,a two-phase medium(saturated soil)under water foundation,a non-flat field(scattering characteristics of circular-arc site),and a second type of stratification(layered boundary crossing the circular-arc site).Main research contents that:(1)The free wave fields in circular-arc two-phase layered saturated site under surface water are derived.The influence of the overlying layer on the site of the saturated medium was introduced,and the reflection and transmission coefficients of the seismic wave at the interface of the saturated soil layer and the soil-water interface were derived.According to the up-going and down-going waves in the medium,the free fields of seismic waves in the site can be obtained.The influence of the incident angle on the reflection and transmission coefficients at different interfaces is analyzed.(2)The scattered wave fields in circular-arc two-phase layered saturated site under surface water are derived.The influence of the non-flat characteristics on the wave field of the site is introduced,and the scattered wave fields with undetermined coefficients are set.The boundary conditions of the site at different coordinate systems are analyzed,and the values of the undetermined coefficients are obtained by mathematical logic derivation.The double-layer saturated medium is degraded into a single-layer saturated medium by formula degradation,which verifies the reliability of the theoretical derivation.(3)The surface displacement of the site is derived.Based on the MATLAB language,a calculation program of the surface displacement of the site was compiled.The comparison with other examples verifies the reliability of the theoretical derivation.The ground vibration characteristics of the layered and non-layered media,and the effects of different incident frequencies and angles on the ground vibration characteristics all are analyzed.