Research On The Computation Model Of The Boundary Stiffness Of Zoned Non-Homogeneous Soil Based On The Scaled Boundary Finite Element Method

The computation of the boundary stiffness of semi-infinite soil has always been animportant research content in the field of structure soil interaction,and a large number of studies have shown that the influence of complex semi-infinite soil on the superstructure can not be ignored.The scaled boundary finite element method(SBFEM)is an effective method to solve the boundary stiffness of semi-infinite soil.Compared with the finite element method,SBFEM only needs to discretize the boundary of the domain and greatly reduces the amount of calculation,and compared with the boundary element method,it does not need the basic solution,which greatly reduces the mathematical complexity and uncertainty.Scaling center is an important geometric feature of this method,which can be defined by point,line and so on.The whole ground needs to be regarded as a whole when solving its stiffness matrix,but for the zoned non-homogeneous soil,such as block soil whose dividing lines of different material zones can not be intersected at the same point and horizontal layered soil resting on half space,the position or type of the scaling center of each subdomain is different,so it is always difficult to establish a unified scaling center for the whole ground and can only be approximated by changing the geometric position of the interface between different zones or by using artificial boundary conditions on some subsoil.For this kind of soil,the SBFEM computation model of the boundary stiffness matrix of zoned non-homogeneous soil was established in this paper,and the computation program of static and dynamic stiffness matrix was compiled to solve the boundary stiffness problem of zoned non-homogeneous soil.The detail content was summarized as follows:1.Aiming at the problems of standard SBFEM in solving the zoned non-homogeneous soil,a piecewise straight line or piecewise curve which is parallel to the structure-soil interface was proposed as the scaling center.This new method can make the radial coordinate axis coincide with the interface between different zones,so that the displacement and stress at the interface satisfy the continuity conditions and the inhomogeneity of zoned soil can be simulated reasonably.2.The scaled coordinate relationship between the scaling line,the soil boundary and the arbitrary point in the computational domain was established based on the scaled boundary transformation of geometry.3.The SBFEM governing equations expressed by displacement,static and dynamic stiffness matrix were obtained by weighted residual technique.Being different from the traditional scaled boundary finite element method,the coefficient matrices in the governing equation is no longer a constant,but a function of the radial coordinates.In this paper,numerical solutions of the boundary static and dynamic stiffness matrix were obtained by using the Runge-Kutta algorithm.4.The validity and effectiveness of the proposed algorithm were verified by calculating the static and dynamic stiffness matrix of the homogeneous semi-infinite soil and the dynamic stiffness matrix of the horizontal layered soil resting on half space.And based on the proposed algorithm,the dynamic stiffness matrix of concrete strip foundation and zoned non-homogeneous soil interaction system was solved.Meanwhile,the influence of the subzone inhomogeneity of the soil material,the difference between the approximate calculation of the standard SBFEM and the result of the proposed algorithm were analyzed.Numerical examples show that: 1)The subzone inhomogeneity has a significant influence on the dynamic stiffness of each direction.Moreover,there are obvious differences between the dynamic stiffness matrices corresponding to different subzone inhomogeneity.2)The results of proposed algorithm in this paper are different from the approximate calculation results of standard SBFEM,and if the soil inhomogeneity is more significant,the approximate interface is more deviated from the actual material interface or the soil scale is bigger,the difference between these two methods will be more significant,which shows the necessity of the proposed algorithm for solving the problem of the boundary stiffness of the zoned non-homogeneous soil.