Eigenvalue Problem of Consolidation

Abstract

Following the preceding paper, the discussion in this paper will be that the governing equation of the multi-dimensional consolidation expressed in terms of the excess pore water pressure alone, can be treated analytically through the eigenvalue problem similar to that of the one-dimensional case. Especially, we will emphasize the importance of the first eigenvalue for the practical application of this theory. The main conclusions of this study are : (1) We can find a set of eigenvalues and eigenfunctions of the multi-dimensional consolidation quite similar to those derived from Terzaghi's one-dimensional equation. (2) The magnitude of the eigenvalue is proportional to the dissipative energy due to the seepage flow. (3) The degree of consolidation is mostly determined by the first eigenvalue and therefore it can be used to estimate the effectiveness of the sand drain as an application.