The analysis of consolidation by a quasi‐Newton technique

Abstract A quasi‐Newton algorithm is implemented for the solution of multi‐dimensional, linear consolidation problems. The study is motivated by the need to implement an efficient equation‐solving technique for the solution of large systems of equations typical in problems of consolidation of saturated porous media. The proposed procedure obviates the need to reassemble and re‐factorize the global coefficient matrix every load increment, albeit the time step may be held variable in the analysis. The method employs the combined techniques of ‘line search’ and BFGS updates applied to the coupled equations. A numerical example is presented to show that the proposed method is computationally more efficient than the conventional direct equation‐solving scheme, particularly when solving large systems of finite element equations.