A coupled meshless-SBFEM-FEM approach in simulating soil-structure interaction with cross-scale model

Highlights

• This paper presents a modified RPIM function and significantly improve the accuracy of interpolation near the boundary.

• The meshless interface is extended to simulate the interface with circular (cambered) types' interfaces.

• Through the object-oriented programming the meshless interfaces and SBFEM is integrated to FEM frameworks.

• The coupled Meshless-SBFEM-FEM can effectively achieve the multilevel cross-scale model in SSI problems.

• Several examples have confirmed the accuracy and flexibility of the proposed Meshless-SBFEM-FEM.

Abstract

This paper presents an integrated, customized routine that uses object-oriented programming and a “super element class” to apply an integrated approach to simulate soil-structure interaction (SSI) problems. The scaled boundary finite element method (SBFEM) and finite element method (FEM) are applied together with the quad tree technique to implement cross-scale modeling for solid elements. Meanwhile, the meshless interface seamlessly connects mismatched and differing sizes of meshes between the soil and the structure, thus allowing cross-scale modeling at the interface level. In addition, through modify the radial point interpolation function (RPIM) and the method of searching supporting nodes, the precision near the boundaries of meshless interface are improved, and circular (cambered) type interfaces can be simulated. Thus, through a coupled Meshless-SBFEM-FEM approach, a fine analysis of soil-structure interaction problem with multilevel cross-scale model can be conducted.

Introduction

In a phenomenon called the contact problem, the combined effects of inner and exterior loads can cause uncoordinated deformation between regions of different media. In practical geotechnical engineering, the phenomenon exists extensively in structure-structure contact problems [1], structure-soil contact problems [2], and soil-soil contact problems [3]. Due to the significant difference in mechanical characteristics, the interface between soil and structure may open, close and slip [4], etc. under static and dynamic loads. The structure-soil contact problems are the most important and complex among the listed problems. In addition, in numerical analysis methods such as finite element modeling, a reasonable simulation must carefully consider the interface zones in SSI problems.

The ability to obtain a high-accuracy response of a structure is of great importance in SSI problems, and such a high-accuracy response is accomplished through the use of fine meshes in structure zone. With the conventional FE model, the refined structural meshes can greatly increase the number of elements throughout the entire model, which may decrease computational efficiency. In previous papers, several approaches have been presented to attack this issue. One widely used method is to gradually increase the mesh density as one gets closer to the interface [5]. However, this method requires excessive manual intervention and is not suitable for 3D modeling. Zhang and Song [6,7] applied the SBFEM-FEM to simulate the progressive damage of structures. Chen et al. presented an optional method that couples SBFEM [[8], [9], [10], [11]] and quad trees to achieve cross-scale modeling and extended their usage to nonlinear materials. The above researchers aimed at achieving cross-scale modeling in solid elements (soil and structure).

In addition, the contributions to the interface are achieved include simulating the interface zone with Goodman elements with zero thickness or finite thickness [3] or with thin finite elements [12,13] as proposed by Desai et al. Since the interface element (i.e. Goodman element and thin finite element) can work with various constitutive models [[15], [16], [17], [18]] to capture the complex soil-structure interaction, the interface element is widely applied to practical geotechnical engineering [2,19,20]. However, the interface elements mentioned above require that the nodes on each side of the interface to be strictly matched. This node-to-node interface element can bring significant restrictions to solving SSI problems. Xing and Song [21,22] presented an SFBEM-based method to convert non-matching node interfaces into node-to-node interfaces for 2D and 3D frictional contact problems. However, the nodal insertion can sometimes complicate modeling operations, especially for 3D models. Meanwhile, this method cannot employ elastic-plastic interface constitutive models. An interface model with asymmetric nodes was developed by Qu et al. [23,24] and successfully applied in concrete face rock-fill dams (CFRDs). This approach also requires partly matching nodes at the boundary of each interface element. Gong et al. extended the meshless method [[25], [26], [27]] to interface zones. Through introducing the RPIM function [[28], [29], [30]], a non-matching node interface was achieve to effectively simulate soil-structure interactions [31].

However, the above meshless interface can only be applied to linear shape interfaces at this stage and the precision significantly decreases near boundaries due to the lower density of nodes in the supporting domain of gauss points near boundaries, which will be further discussed in the following sections. In this paper, an enhanced meshless interface is developed to overcome the disadvantages mentioned above through: (1) Introducing circular type background mesh lines to satisfy the interface shape and modifying the searching method to extend the method towards application to circular (cambered) type interfaces. (2) Adding virtual nodes near the edge of interfaces and combining the linear interpolation to produce a significant improvement in accuracy near the boundaries of interfaces.

In this paper, SBFEM is applied to achieve the cross-scale modeling in solid elements [[8], [9], [10], [11]], and the enhanced meshless interfaces can connect soil and structure models that possess different sizes of meshes, which can achieve cross-scale modeling at the interface level [31]. Together with the above techniques, a multilevel cross-scale model can be established, which is of great significant in refined analysis. However, due to different approaches in solving shape functions, stiffness matrices, internal and external force vectors across each method, it is challenging to achieve a coupling of the methods and none papers have coupled the above three methods to solve SSI problems. However, through object-oriented programming and the “super element class”, the SBFEM and the meshless interface can be integrated into the custom developed FEM platform described in this paper. Thus, a highly flexible and effective method that enables a coupled Meshless-SBFEM-FEM approach is presented to implement multilevel, cross-scale modeling for SSI problems. The introduced method is also effective for independent meshing and local mesh optimization problems.

The remainder of this paper is organized as follows. The derivation and numerical implementation of Meshless-SBFEM-FEM is shown in section 2. Two numerical examples are presented in sections 3.1 Simulating footing-soil interaction, 3.2 Simulating a buried pipe to verify the improved performance of the enhanced meshless interface. In sections 3.3 Simulating a frame metro structure, 3.4 Simulating a three-arch type metro structure, the enhanced meshless interface coupled with FEM and SBFEM is applied to the simulation of metro structures (e.g. frame metro station, three-arch column type metro station) for fine damage analysis. Finally, section 4 summarizes the major conclusions in this paper.