Extension of explicit Runge-Kutta substepping stress integration for viscoplastic model of saturated soils

Abstract

Stable integration schemes are critically important for rate-dependent constitutive models, serving as a cornerstone for ensuring accuracy, efficiency, and robustness in finite element implementations. This paper investigates the numerical performance of explicit stress integration schemes with adaptive substepping for integrating a newly proposed fractional consistency two-surface viscoplastic model for saturated clays. The incremental stress–strain-strain rate relation of the model can be linearized following the consistency condition of the rate-dependent loading surface and subsequently integrated using four distinct explicit Runge-Kutta substepping integration algorithms (i.e., RK12, RK23, RK34, RK45) with automatic error control and stress drift correction techniques. The overall numerical performance of the algorithms in terms of accuracy and efficiency is evaluated at both the material point level (i.e., isotropic, oedometric, and triaxial compression tests) and the boundary-value problem level (i.e., piezocone penetration and underground gallery excavation), which demonstrates that the RK23 and RK34 algorithms perform excellently in balancing accuracy and computational cost. The proposed algorithms provide a versatile and adaptive framework for integrating time-dependent constitutive equations, particularly those based on the consistency viscoplastic approaches commonly used in advanced rate-dependent modeling, allowing for a wide range of geotechnical engineering applications.