Research On The Scaled Boundary Finite Element Method For Stiffness Of Foundation In 3D Heterogeneous Soil

In the seismic response analysis of large structures such as dams and nuclear power plants,the interaction between structures with infinite soils needs to be considered,and the solving stiffness of foundations on infinite soils is a core content of transactional analysis.Although the boundary element method,the thin layer method,analytical layer-element method,and mixed variable method and other methods can be effectively applied to the 3D homogeneous or horizontal layered semi-infinite soils,the soils of the structures may be complex geological and topographical soils,such as the 3D non-horizontal layered partitioned semi-infinite soil,3D partition infinite long valley soil.It is difficult to accurately calculate the stiffness of foundations on these complex soils by the above methods.The scaled boundary finite element method(SBFEM)is a semi-analytical and semi-numerical method developed in recent years to solve partial differential equations.This method can effectively simulate the radiation damping effect in infinite domain.In this article,a new kind of SBFEM with a plane parallel to the soil boundary as the scaling center is proposed.The method in this paper can ensure the continuity of displacement and stress at the interface of each partition in the complex partitioned soil,can be applied to the 3D non-horizontal layered partitioned semi-infinite soils and 3D partitioned infinite long river valley soils with the characteristic of complex partitions which are difficult to be solved by existing methods.,and broadens the applicable scope of SBFEM.The core contents of this article as follow:1.Based on the standard SBFEM with point as scaling center,the SBFEM with surface as scaling center is proposed in this article.Firstly,the defining method of scaling central surface is given;based on the principle of radial scaling and circumferential discretization,the coordinate relationship between any point in the domain and the corresponding point on the similar central surface and foundation boundary is established;based on Hamilton principle,the governing equations of the static and dynamic boundary stiffness matrixes of foundation on the 3D infinite soils are derived.2.Compared with standard SBFEM,the scaling center of the method in this paper is the surface,the coefficient matrixes in the governing equations of boundary stiffness are no longer constant matrixes,but a function of local radial coordinate,and the governing equations become ordinary differential equation with first order variable coefficient.Referring to the high frequency progressive expansion method in standard SBFEM,and aiming at the solving control equations of boundary stiffness obtained by the method in this paper,the corresponding solution idea is put forward: Firstly,the expressions of the stiffness matrixes at infinity is given,and then plug the expressions into corresponding governing equations and work out them,taking them as the initial value,then the static and dynamic stiffness matrixes at the interface between structures and soils are obtained by runge-kutta algorithm.3.The method is used to calculate the boundary stiffness of foundation on 3D homogeneous semi-infinite soil,3D horizontal layered semi-infinite soil and 3D infinite long river valley soil,compared with the results of thin layer method and boundary element method and the numerical integral method,the accuracy and validity of the method and program code presented in this article are verified.4.The 3D non-horizontal layered partitioned semi-infinite soils and 3D partitioned infinite long river valley soils with the characteristics of complex partitions are difficult to be calculated by the existing methods.The boundary stiffness of foundation on above soils under different partitioned conditions are calculated by the method presented in this article,and the influences of partitioned heterogeneity on the boundary stiffness of the soils are studied.The results show that: the partitioned heterogeneity of 3D infinite soil has significant effect on the boundary stiffness of foundation on soils,the boundary stiffness of foundation on soils in different partitioned conditions are obviously different.Therefore,in the analysis of the interaction between the actual structures and the soils,the actual condition of soil partition should be considered.