Abstract: Aimed at the ill-conditioned problem of Biot’s consolidation finite element method (BCFEM), both orthogonal test and dimensional analysis method are used to study the ill-conditioning regularity and its influencing factors. The influencing factors such as the average size of finite element, the length of timestep, the compressibility of soil and the permeability of soil are taken into account. Two groups of independent similarity criteria are proposed, on the basis of which, two novel dimensionless variables are obtained to analyze the variation of the condition number of BCFEM coefficient matrix. Through the parametric study of an illustrative case, the results show that the average size of finite element, the length of timestep, the compressibility of soil and the permeability of soil are in the order of priority of sensitivity. The smaller the averaged size of finite element, the worse the ill-conditioning situation of BCFEM. With the increase of the presented dimensionless variables, the ill-conditioning number shows a tendency to increasing, etc. The conclusions are helpful to study the ill-conditioned problem of BCFEM.

Key words: Biot’s consolidation theory, finite element method, ill-conditioned problem, orthogonal test, dimensional analysis