Analytical Integrations for Three-dimensional Fictitious Stress Method Based on Kelvin Solution.

Recently, and elastic analysis by three-dimensional boundary element method based on fictitious stress method, in which the numerical integrations have to be used to get the influence coefficients, is extensively applied and studied. However, to analyze three dimensional models of natural geological structure and artificial underground excavation or for a large scale computation of stress and displacement and stability evaluation using their combined model, exploitation of much more accurate and faster analytical solutions in order to avoid numerical integration is regarded as extremely valuable. Kuriyama and Mizuta have carried out the study in which, however, the elaborate integration results seem complicated. Furthermore, if some observed points were located at the elongated line of one side of a triangular element (these points are regards as special observed ones), their analytical integrations can not be applied. In other words, the singular point (the center of gravity) and the special points (on the elongation of three sides) have to be evaded when using the analytical codes developed by Kuriyama and Mizuta. This is usually not realistic in a huge model. Therefore, the corrected and much more concise analytical integrations for arbitrary boundary shapes, arbitrary divisions of triangular elements and arbitrary observed points (except the three sides of triangular) are deduced in this paper.