The Research Of Wave Propagation And Seismic Response Of Underground Structures In Complex Layered Soil

Urban underground rail transit and underground pipe galleries play an important role in urban life and production.Once the underground structure is destroyed,it will have a huge impact on the residents' lives and seriously threaten the lives of the residents.Strong earthquakes are an important factor causing serious damage to underground structures and may cause serious secondary disasters such as floods,urban waterlogging,and fires.Therefore,accurate and efficient seismic safety evaluation of underground structures is an important issue for engineering designers and scientific researchers.The seismic analysis of underground structures is generally treated as a wave scattering problem.The calculation models of wave scattering in the extending literature mostly assume that the soil is single-phase,isotropic,homogeneous medium.The natural soil is much more complex,such as layered distribution,anisotropy,and groundwater.From the research status of the wave scattering problem,the existing algorithms often have certain limitations,such as not suitable for considering layered foundations,difficult to solve anisotropic material,difficult to solve saturated media and so on.Therefore,this paper presents a substructure model of underground structure,which can easily consider a variety of complex factors and accurately solve the seismic response of underground structures in complex layered foundations.Based on the substructure method,the complex scattering problems are transformed into a radation problem and the evaluation of wave response of layered half-space with regular boundary conditions.Compared with the solution of scattering waves caused by complex geometric boundary conditions,it is much simpler to solve the radiation problem and the wave response problem of the rule boundary condition half-space,and this conversion is completely accurate for the linear elastic medium without introducing any simplification.When the radiation problem and the wave response problem of the ground with the regular boundary conditions are solved with high precision,the solution to the complex site scattering problem is also highly accurate.The accuracy of the substructure model is verified by various examples,such as the scattering of SV and P waves by underground holes in homogeneous half space.To the best of our knowledge,there are a few high-precision solutions for the seismic response of underground structures in layered half-space,especially for transversely isotropic layered half-space.Therefore,based on the numerical model of this paper,Numerical experiments have been carried out to provide a large number of high-precision numerical examples.(1)The Green's function of isotropic and transversely isotropic layered soils is derived,and the numerical solution is given to further obtain the dynamic stiffness of the internal nodes.The Fourier transform is used to obtain the wave equation in the frequency domain-wavenumber domain of single-phase isotropic and transversely isotropic media.The dual variable is introduced to reduce the wave equation to the first-order ordinary differential equation,and the soil layer is merged by using the extended precise integration algorithm.The load boundary condition is applied to obtain the Green's function,and the dynamic stiffness is obtained.Based on the extended precise integration algorithm,the coefficient matrix of the improved transfer matrix method is given,and the Wave Motion of the single-phase isotropic and transversely isotropic layered half-space is calculated.The accuracy and effectiveness of the proposed method are validated by comparing it with the results of extant studies.The scattering effects of horseshoe holes embedded in complex layered half-space are investigated and the effects of material anisotropy,surface weathering layer and other factors on the wave response of complex lining structures are discussed.(2)The Green's function and dynamic stiffness of isotropic and transversely isotropic saturated layered sites are obtained.Based on Biot's poroelastodynamic equations,the displacement of the pore fluid is eliminated,and the governing equation use the solid skeleton displacement and pore-fluid pressure as the unknown variables.The Fourier transform is applied to transform the wave motion equations from frequency-spatial domain into frequency wave-number domain.The generalized dual variable is introduced,and the first-order state equation is achieved.The dual relationship between the layers is established according to different surface drainage conditions.Finally,the boundary conditions are applied to obtain the dynamic response of the buried loading,and the dynamic stiffness in the frequency-space domain is obtained.The accuracy of the method is verified by numerical examples,and the influence of the anisotropy of the foundation material on the dynamic stiffness of the saturated layered half-space is discussed.(3)The dynamic stiffness of arbitrarily shaped rigid foundation embedded in partially multi-layered saturated half-space is evaluated.The proposed method can conveniently consider different drainage conditions of the interface between the saturated soil layer and the single-phase soil layer,and is applicable not only to the isotropic medium but also to the transversely isotropic medium.The accuracy of the method is verified by comparison with the methods in the existing literature.The influence of the shape of foundation on the dynamic stiffness of the rigid strip foundation is further discussed.From the calculation results of this paper,the shape of the buried foundation has a significant influence on the dynamic stiffness of the rocking direction and less on the horizontal direction dynamic stiffness.(4)Based on the extended precise integration algorithm,the coefficient matrix of the improved transfer matrix method for partially saturated multi-layered half-space is derived,and the wave propagation in the free field of partially saturated multi-layered half-space is calculated.A calculation model is proposed to evaluate the dynamic response of a structure embedded in partially saturated multi-layered half-space.The accuracy of the method is verified by numerical examples.The scattering effects of the two-layer lining tunnel on the SV wave and P1 wave in the partially saturated layered half-space are investigated.