A Stable Explicit Method With High Order Of Accuracy Of The One Dimensional Seismic Response Of Layered-Soil

The analysis of seismic reposnse of layered solis and the sesmic hazard of site earthquake meeting the basic problem.There are two main mehods to solve the problem: one is based on the exact solution,which is simplified to a one-dimension horizontal shearing bar,adopting the reflection and transmission of wave motion on boundaries surface of for frequency domain analysis, derivating the transfer matrix of amplitude coefficient for any two layers,if encountered the nonlinear media,which is used equivalent linear of method;The other is based on time domain analysis,adopting the Finite element method. In most instances,the former,considering the nonlinear media for engineering,using the equivalent linearization method in frequency analysis can cause large errors.With the growing of computer science,the latter has been widely applied in the design of large and complex engineerings.Based on literature [61],the existing time-space decoupling explicit finite element mehod,the model of seismic response of layered media converts into the analysis of one-dimensional shearing bar model, this paper is devoted to exploring explicit methods with high order of accuracy in time domain for the numerical model of wave motion,the main research contents are as follows:(1) Simplifying one-dimensional stratified soil layer model of one-dimensional shear bar, which is owing to the problem of the one-dimensional wave equation,basing on analytical solution of one-dimensional wave equation (D'alembert solution), are presented by an explicit recursive formula which is only used polynomial interpolation in space,integraling exactly in the time domain with 6-order of accuracy.The new recursion formula proves that it is stable and computational efficiency of the three aspects of analysis, and the numerical test of the sixth-order explicit formula of the precision, stability and efficiency of the verification, illustrates the higher order accuracy recursion formula both in time and space step away from the increasing still has lower accuracy formula in the original space and time step from the numerical calculation accuracy, verify the order of accuracy improvement for increasing the order of numerical simulation computational efficiency of importance.(2)The six-order explicit recursive formula is compared with the common numerical simulation method,and the accuracy and stability of the numerical simulation method are compared by numerical experiments.(3)Based on interface points' analytical solution in a short time window, which is deduced by combination of the fact about the finiteness of wave velocity and the solutions of Cauchy problem of wave equation, a method of constructing an high order explicit recursion formula for interface points is provided for numerical simulation of scalar wave motion in uniformly layered model. In view of the layered medium model in the field of earthquake engineering, the explicit recursion formula of the one dimensional seismic response of layer-soils is presented...