Numerical solution of a non-linear model for self-weight solids settlement

The present study proposes a 1D model that describes the solids consolidati on process occurring in a saturated sediment column due to its own weight. The governing consolidation equation, a second order non-linear transient p artial differential equation of the parabolic type with the effective stres s as the dependent variable, is solved by using the finite element and fini te difference methods. In the spatial discretization of the problem, the Pe trov-Galerkin method is used to obtain the weak form of the equation. For t he model's time discretization, two timing step schemes are used for the sa ke of comparison: the Crank-Nicolson and the backward-difference schemes. T he contribution of the non-linear terms is determined by employing the stan dard Newton-Raphson iteration method. The present formulation and numerical approach are examined by using the results of two consolidation tests, an attapulgite solids column and a mixture of kaolin-bentonite solids column. The comparison shows that the consolidation rate and the distribution of th e volume fraction of solids within the columns can be accurately predicted by the present model. In addition the results of the non-linear model are c ompared with those of the corresponding linear consolidation model. It is s hown that the linear model significantly overpredicts the rate of consolida tion. Finally, the effect of the initial conditions on the model prediction s is also examined. (C) 1999 Elsevier Science Inc. All rights reserved.