Green函数在BEM(boundary element method)计算中的降维效应、积分方程的数值直接求解和奇异解自动满足无穷远辐射条件,这些在土动力学计算问题上独特的优点,早已被研究者认同.但在计算机技术迅速发展的今天,面向对象编程在广泛开拓与应用,Green函数能在计算技术上简便地集成与抽象,实现简约编程,却一直未被发现.该文根据已有的土动力问题的Green函数计算方法,对Green函数进行了OOP(object-oriented programming)条件下的再抽象与集成.提出面向对象的计算过程,并根据作者得到两相饱和介质Green函数,成功地计算了波场法的饱和土隧道中的动力反应问题,并给出时程曲线与瞬态的振动解答.
It has been generally recognized that Green function integrated with Boundary Element Method (BEM) has advantages in dimensional reduction, high accuracy and satisfaction of the radiation condition at infinity, etc. Recently, the computational technique has rapidly developed and the orient-object programming has been widely applied, whereas the attribute of abstraction and the integration of Green function employed in BEM have not been discovered yet. In this work the abstraction and integration of Green function are carried out for soil dynamics problems, and the procedure of the object-oriented calculation method is presented. Based on the Green function developed for the two-phase saturated medium, the response of the wave field to tunnel subjected to dynamic loading is calculated, and the transient solution as well as the time history of response is obtained.
The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space.
Boyang Ding,and Jun Chen College of Civil Engineering and Architecture,Zhejiang University of Technology,Hangzhou 310014,China
When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.
