The effects of geotechnical material properties on the convergence of iterative solvers

There is increasing interest in the use of iterative rather than direct solvers for geotechnical finite element analysis. For large 3D problems iterative solvers offer the only possibility of economical solution on a desktop PC. The major stumbling block with iterative solvers is ensuring fast convergence to a suitably accurate
solution. The system of equations is always “preconditioned” to improve convergence and the design of preconditioners is a current hot topic in many areas of computational engineering. Effective preconditioning for geotechnical FE is particularly difficult due to (a) the wide range of elasto-plastic constitutive models used and (b) the changing nature of the equations during analysis (due to development of zones of plasticity for instance). In this paper we examine the features of some elasto-plastic material models that affect convergence of iterative solution methods, focussing on analysis of condition numbers of stiffness matrices. It is well-known that frictional material models lead to unsymmetric systems of equations and here we examine the role of the angle of dilation on system condition. The use of the consistent constitutive matrix, instead of the standard constitutive matrix is shown to have an effect on the condition numbers of the systems to be solved.