A Method For Layered Half-space Site Response Under Obliquely Incident Earthquake And Its Application

Seismic response analysis of underground subway structures usually uses the timedomain method combining finite element method with viscous-spring artificial boundary. The site seismic response need to be calculated before analysis, and it is then transformed into equivalent earthquake loading at artificial boundary. Sedimentary site of the underground subway structures can be simplified to layered half-space. When the moderate distance between the site and the epicenter of shallow earthquakes occurs, the seismic input can be simplified as plane body wave of oblique incidence. The transfer matrix method and stiffness matrix method are the classical methods of calculating site response of layered half space with oblique incidence seismic wave. However, both of them are based on analytical solutions in frequency domain, which are not suitable for the nonlinear problem. The time-domain method such as finite element method, is available for resolving the problem of nonlinear problem, but it fails to simulate the propagation of plane wave in half-infinite two-dimensional space. This paper presents a one-dimensional finite element artificial boundary method to calculate the response of layered half space site under seismic plane wave of oblique incidence. This method is further applied to analyze seismic response of underground subway structures and to study the effect of seismic wave incidence angle and soil layer characteristic on the structural seismic response. The works are as follows.1. A one-dimensional finite element artificial boundary method is proposed to calculate the response of layered half space site under seismic plane wave of oblique incidence. In this method, the homogeneous half space bedrock is cut off, and its wave radiation and input effects are modelled by an exact artificial boundary condition combining absorbing boundary condition and input boundary condition; secondly, the horizontally infinite two-dimensional problem can be transformed into a onedimensional problem along the depth direction by using Snell law; and lastly, the resulting one-dimensional problem can be solved by the explicit dynamics finite element method that can take into account non-diagonal damping matrix. A MATLAB program for this method is written. The seismic response analysis of several classical sites showed that the result of this method coincided well with the result of method combining transfer matrix method and Fourier transform, which proved the validity of this method.2. Seismic response of site is inputted at the artificial boundary. Firstly, according to Snell Law, site seismic response is extended from one dimensional space into two dimensional space; secondly, the earthquake load acting on artificial boundary is obtained by the equivalent load method based on viscous-spring artificial boundary condition; lastly, the FORTRAN programs are written to apply viscous-spring artificial boundary condition and earthquake load in ABAQUS finite element software. It verifies the correctness of site seismic response input in ABAQUS software by coMParing the result of two-dimensional site with the result of one-dimensional finiteelement artificial boundary method.3. Taking a subway station for example, on the basis of ABAQUS software, the seismic response of underground subway structures is analyzed by considering the oblique incidence of plane seismic wave and the characteristics of layered half-space. Then, the effect of oblique incidence angle and changing soil characteristics on the responses of subway station structure is studied.