Assessing the accuracy and efficiency of different order implicit and explicit integration schemes

Abstract

A first order accurate fully implicit integration scheme and four different order explicit substepping integration schemes with automatic error control are used in this paper to integrate the constitutive relations of a critical state model for saturated soils. Their respective computational performance in terms of accuracy and efficiency is assessed in order to provide practical guidance for deciding which of the five is most suitable for solving numerical problems in geotechnical engineering involving critical state models. Even though existing literature of integration schemes applied to geotechnical problems has traditionally been focussed on the first order accurate implicit backward Euler and on the second order accurate explicit modified Euler with substepping almost exclusively, the findings of this paper suggest that the little extra work required in the implementation of an explicit third order Runge-Kutta substepping scheme is worth the effort, especially in terms of computational cost.