Finite element consolidation analysis of soils with vertical drain

This paper presents a finite element procedure for the analysis of consolidation of layered soils with vertical drain using general one-dimensional (1-D) constitutive models. In formulating the finite element procedure, a Newton-Cotes-type integration formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (Modified Newton) iteration scheme. The proposed procedure is then applied for the consolidation analysis of a number of typical problems using both linear and non-linear soil models. Results from this simplified method are compared with those from a fully coupled consolidation analysis using a well-known finite element package. The average degree of consolidation, excess porewater pressure and average vertical effective stress are almost the same as those from the fully coupled analysis for both the linear and non-linear cases studied. The differences in vertical effective stresses are tolerable except for the values near the vertical drain boundaries. The consolidation behaviour of soils below a certain depth of the bottom of vertical drain is actually one-dimensional for the partially penetrating case. Therefore, there are not much differences in whether one uses a one-dimensional model or a three-dimensional model in this region. The average degree of consolidation has good normalized feature with respect to the ratio of well radius to external drainage boundary for the cases of fully penetrating vertical drain using a normalized time even in the non-linear case. Numerical results clearly demonstrate that the proposed simplified finite element procedure is efficient for the consolidation analysis of soils with vertical drain and it has better numerical stability characteristics. This simplified method can easily account for layered systems, time-dependent loading, well-resistance, smear effects and inelastic stress-strain behaviour. This method is also very suitable for the design of vertical drain, since it greatly reduces the unknown variables in the calculation and the 1-D soil model parameters can be more easily determined.