Complete and semi-complete explicit algorithms of a unified critical state model for over-consolidation clays

This paper presents a comparison of the performance of explicit algorithm and semi-complete explicit algorithm in the numerical implementations of an unconventional plastic model for soils. The new model, named CASM-S, is developed by incorporating the sub-loading surface theory into the standard unified clay and sand model (i.e., CASM), to enhance the prediction ability for the mechanical behavior of over-consolidated soils. The complete explicit algorithm of CASM-S is based on the sub-stepping method with the technique of automatic error control (SUBM), while the semi-complete explicit algorithm adopts the cutting-plane integration procedure (CPM). The complete implementation process of this model is performed, and the stability, accuracy, and efficiency of these two algorithms are compared through a series of numerical simulations, such as fluid-structure coupling problem, over-consolidation problem, and square-footing problem. These simulations demonstrate that CASM-S implemented by both the SUBM and CPM can obtain a reliable solution under appropriate size of increments. For the sub-loading surface model with highly nonlinear characteristics used in this paper, the CPM has faster local convergence rate, but the SUBM shows a higher efficiency and accuracy at global level.