Research On Wave Scattering Of Holes In Complex Layered Sites Based On Scaled Boundary Finite Element Method

Site response analysis of a complex layered site has become one of the research focus areas recently.In contrast to the assumption of homogeneity and isotropy soil often used in the literature,a complex,layered site can better describe the problems in actual projects.Many studies have confirmed that the complex layered site conditions will certainly affect the geometry and intensity of seismic waves.If there are scatterers such as underground holes and excavations in the site,the distribution of the ground motion will be more complicated compared with the homogeneous site,and the dynamic response of the surface buildings will also be affected.In the past two to three decades,with the innovation of computing tools,many numerical methods for solving wave scattering problems have been proposed in the literature.These methods usually obtain ideal results at low frequencies,but the error increases as frequency increases.In this paper,the scaled boundary finite element method is used to study the analysis method of the dynamic response of the structure-layered soil system with incidence of seismic wave.The scaled boundary finite element method(SBFEM)is a semi-analytical algorithm for solving partial differential equations and is especially suitable for wave propagation problems in the infinite domain.The original scaled boundary finite element method is based on the use of a scaling center to transform from Cartesian coordinates to scaled boundary coordinates,such that the problem can be solved numerically in the circumferential directions and analytically in the radial direction.Thus,the spatial dimension of the problem is reduced by one and radiation damping in the unbounded domain can be modeled accurately.As a result,the scaled boundary finite element method is particularly suitable for the analysis of wave scattering problems in unbounded domain.However,the scaled boundary transformation based on the use of a scaling center cannot accurately describe the geometry of layered sites and limits the application of the method.Recently,based on the use of a scaling line instead of a scaling center,a modified version of the scaled boundary transformation is proposed,which overcomes the shortcomings of the original scaled boundary finite element method to a certain extent.However,the research on the modified scaled boundary finite element method is still in its infancy,and has not been put into use of the scattering analysis of complex site.In this paper,based on the substructure method,the modified scaled boundary finite element method and the transfer-matrix method are used to establish the method of solving the wave scattering problem of the structure-layered soil system.The main work of this paper includes:1.Based on the substructure method of the soil-structure interaction,the scaled boundary finite element method with a scaling line and the transfer-matrix method of seismic response of free field in a horizontal layered site are combined to create an analysis model of dynamic structure-layered soil interaction in the frequency domain.The complex layered site is divided into regions: the near field containing many complex factors,such as inclusions,folds,xenoliths,etc.,is simulated by finite element method;the far field can be a horizontal layered site and is simulated by scaled boundary finite element method with a scaling line,which can more accurately simulates the frequency-domain dynamic stiffness of horizontal layered excavation sites.Here,the continuity of displacements and stress across layer interfaces are enforced.In addition,the transfer-matrix method can accurately simulate the response of the free field in a horizontal layered site with incidence of seismic waves.This numerical model is theoretically accurate.2.Based on the structure-layered soil system interaction numerical model,a program for analyzing seismic response of structure-layered soil system using substructure method is compiled.Various numerical examples-including the Green function of the layered site,the dynamic stiffness of the rigid foundation on the ground,the scattering of SV waves in the halfspace with a circular hole and the scattering of an elliptical sedimentary valley in a layered site-demonstrate the accuracy of the numerical model and its correct implementation.3.In order to illustrate that the proposed model has wide applicability,the scattering problems of SV and P waves in layered site with a circular hole or a rectangle hole are analyzed.Numerical examples show that,in a complex layered site,the interlayer impedance ratio and the shape of the hole will affect the distribution of the wave.Especially when the incident wave frequency is close to the site natural frequency,the impact of the impedance ratio on the scattered field wave distribution is significant.The research conclusion can provide technical basis for the design of underground structures.