Solution of soil-structure interaction problems by coupled boundary element-finite element method

Abstract

Soil-structure interaction problems involve the solution of boundary value problems consisting of two domains: A near field finite domain representing the structure and adjacent soil, and a semi-infinite far-field domain representing the soil distant from the structure. Currently, the most used numerical method for solving such problems, the finite element method, considers only the near field, and neglects the effects of the far field. Depending on the domain size considered, this results in significant errors in the computed displacements and stress compared to closed form solutions.

This research develops a numerical method in which both the near and far-field are considered. In this numerical procedure, the far field is assumed to be a homogenous elastic half-plane is modeled using boundary elements based on the Melan fundamental solution. A technique, called the substructure method, for coupling the boundary element method with finite element method is developed. Unlike other coupling techniques, the substructure method preserves the bandedness and symmetry of the system of equations resulting from the finite element method. The substructure method is implemented into a computer for program BEFEC for solving linear elastic and elasto-plastic plane strain problems. The proposed coupling technique is also incorporated into an existing finite element program SOILSTRUCT to perform soil-structure interaction analysis on U-frame lock structures.

A series of analyses performed on the elastic strip footing problem indicate that significant errors occur in the predicted displacements and stresses when the effects of the the far field are ignored. These errors are unaffected by the boundary conditions assumed or the type of finite element used. The analyses demonstrated that the displacements and stresses obtained using the coupled BEM-FEM solution agree well with closed form solutions.

Results of the soil-structure interaction analyses performed on U-frame lock structures indicates that neglecting the effects of the far field domain results in a significant underprediciton of the vertical displacements. These analyses also showed that there are significant differences in the computed shear stress and lateral pressures when the effects of the far field are considered.

Results of the bearing capacity analyses of strip footing on elasto-plastic soils indicate that when the effects of the far field are taken into consideration, initial yield takes place at a higher load level. This in turn results is smaller plastic deformations as compared to the case when the far field is ignored. These analyses also shown that taking into consideration the far field results in significant differences in the computed stresses. These differences are diminished when the effects of self-weight are taken into consideration. The analyses performed on the Rankine earth pressure problem indicate that while the far field does not significantly affect the computed Rankine forces or lateral pressure distribution, much larger wall movements are required to reach both the active or passive States.