Analytical Solutions Of Dynamic Soil-Structure Interaction With Flexible Foundation For Seismic Excitation

Dynamic soil-structure interaction(SSI)is one of the fundamental problems in the field of earthquake engineering.Compared with rigid-foundation,considering foundation stiffness in SSI analysis is more meaningful.However,domestic and foreign research on the effects of foundation stiffness on SSI are still very few.How foundation stiffness influences SSI need to be further studied.This paper adopts two dimensional semi-circular flexible foundation-SDOF model,composite foundation-SDOF model et al embedded in homogeneous half-space under incident plane SH waves,to obtain analytical solutions of foundation response and structural relative response,and analyze how foundation stiffness influence system response and system frequency.Although the models are simple,the essential influence of foundation stiffness on SSI can be revealed.Foundation stiffness significantly influences the foundation response and structural relative response.When foundation is flexible,there is larger foundation response than that of rigid foundation,and there is large out-of-plane torsional foundation deformation,especially for oblique incident waves.The peak of the structural relative response is always smaller than that of rigid foundation,and the system frequency shifts to lower frequency.Relative deformation of foundation will causes additional stress in structure.If mass and stiffness of structure are relative large,foundation still cannot be treated as a rigid foundation even for foundation stiffness many times larger than that of soil(foundation shear velocity is 100 times than that of soil),because there is still significant additional stress in structure.When considering foundation stiffness in the analysis of structure-soil-structure interaction(SSSI),system response is highly dependent on foundation stiffness,foundation distance and incident angle.Even the distance between two foundatons is more than 10 times of foundation size,there is still significant interaction between two foundations.The system frequency of each foundation will occur certain flunctant around the system freqeucy of single flexible foundation.