Time Integration Algorithms for Elasto-Viscoplastic Models with Multiple Hardening Laws for Geomaterials: Enhancement and Comparative Study

Abstract

To describe the behaviours of geomaterials such as time-dependency, anisotropy and destructuration, multiple hardening parameters and laws are generally needed for application in advanced elasto-viscoplastic models. Time integration with stress updating is a key step in the application of elasto-viscoplastic models to engineering practice. However, the robustness of time integration algorithms for such complicated models has rarely been studied, creating difficulties in selecting and improving algorithms. This paper focuses on use of three typical implicit time integration algorithms—Katona, Stolle and cutting plane—for integration of an advanced elasto-viscoplastic model. First, all selected algorithms are improved to fit the characteristics of the advanced model with multiple hardening parameters and are combined with adaptive substepping procedures to enhance their performance. Then a step-changed undrained triaxial test is simulated at the integration point level, on the basis of which variations in iteration number and relative error of stresses with step size are investigated and compared. Furthermore, the advanced model using different algorithms is implemented into finite element code, with global convergence and calculation time investigated and compared for two boundary value problems: a biaxial test and an embankment. All comparisons demonstrate that the modified cutting plane algorithm with substepping is the most robust and efficient one, followed by the modified Stolle with substepping and the modified Katona with substepping, for an advanced model with multiple hardening parameters.