THREE DIMENSIONAL SOIL‐STRUCTURE INTERACTION ANALYSIS: DEFORMABLE STRUCTURES IN MULTILAYERED SOIL MASS

Abstract

A new hybrid method based on three‐dimensional finite element idealization in the near field and a semi‐analytic scheme using the principles of wave propagation in multilayered half space in the far field is proposed for the dynamic soil‐structure interaction analysis. The distinguishing feature of this technique from direct or indirect boundary integral techniques is that in boundary integral techniques a distribution of sources are considered at the near field boundary. Strengths of these sources are then adjusted to satisfy the continuity conditions across the near‐field/far‐field interface. In the proposed method unknown sources are placed not at the near field boundary but at the location of the structure. Then the Saint‐Venant's principle is utilized to justify that at a distant point the effect of the structure's vibration can be effectively modelled by an equivalent vibrating point force and vibrating moment at the structure's position. Thus the number of unknowns can be greatly reduced here. For soil‐structure interaction analysis by this method one needs to consider only three unknowns (two force components and one in‐plane moment) for a general two‐dimensional problem and six unknowns (three force components and three moment components) for a general three‐dimensional problem. When a vertically propagating elastic wave strikes a structure which is symmetric about two mutually perpendicular vertical planes the structure can only vibrate vertically for dilatational waves and horizontally for shear waves. Under this situation the number of unknowns is reduced to only one whereas in boundary integral and boundary element techniques the number of unknowns is dependent on the number of nodes at the near field boundary, which is generally much greater than six. Several example problems are solved in this paper using this technique for both flexible and rigid structures in multilayered soil media.