Dynamic-stiffness matrix of soil by the boundary-element method: Conceptual aspects

TLDR: In this article, the same type of boundary matrices which have a clear physical interpretation are identified in the three boundary-element methods, each of which is illustrated with a simple static example.

Abstract: Starting from a weighted-residual formulation, the various boundary-element methods, i.e. the weighted-residual technique, the indirect boundary-element method and the direct boundary-element method, are systematically developed for the calculation of the dynamic-stiffness matrix of an embedded foundation. In all three methods, loads whose analytical response in the unbounded domain can be determined are introduced acting on the continuous soil towards the region to be excavated. In the weighted-residual technique and in the indirect boundary-element method, a weighting function is used; in the latter case, it is selected as the Green's function for the surface traction. In the direct boundary-element method, the surface traction along the structure-soil interface is interpolated. The same type of boundary matrices which have a clear physical interpretation are identified in the three formulations, each of which is illustrated with a simple static example. The indirect boundary-element method leads to the most accurate results. The guaranteed symmetry and the fact that the displacement arising from the applied loads can easily be calculated and compared to the prescribed displacement makes the indirect boundary-element method especially attractive for calculating the dynamic-stiffness matrix of the soil. Instead of calculating the dynamic-stiffness matrix of the embedded foundation with the boundary-element method, it can be determined as the difference of those of the regular free field and of the excavated part. The calculation of the former does not require the Green's function for the surface traction. The dynamic stiffness of the excavated part can be calculated by the finite-element method.