A nonlinear viscoelastic-plastic creep model for silty mudstone considering critical damage state

• The triaxial compressive and graded loading characteristics of silty mudstone subjected to various stress levels are explored. • A nonlinear viscoelastic-plastic creep constitutive model (MKNVPB) for silty mudstone considering critical failure state is developed. • Implemented secondary development of the MKNVPB model into three-dimensional differential form in FLAC 3D . • Conducted comparative analysis between numerical simulations replicating test paths in FLAC 3D and experimental results. Accurate prediction of creep deformation within rock mass is critical for the long-term stability analysis of soft rock slopes. To address current modeling limitations for silty mudstone under critical damage conditions, conventional triaxial and multi-staged loading tests were performed on artificial analog material specimens whose physical-mechanical properties closely mimic those of natural silty mudstone. Experimental observations revealed an enhancement in strength and stiffness occurred at higher confining pressure ( σ 3 ). Moreover, higher σ 3 could delay the onset of specimen failure while pronounced instantaneous deformation and accelerated creep behaviors emerged at higher deviatoric stress ( σ d ), accompanied by evident reductions in long-term strength ( σ s ). Leveraging the Unified Rheological Mechanical Model Theory integrating a long-term strength switch function and a critical damage threshold, a novel nonlinear viscoelastic-plastic constitutive model termed modified Kelvin nonlinear viscoplastic body (MKNVPB) was developed, which can capture structural deterioration through a damage evolution variable. Model parameters were inverted from experimental data using a global optimization algorithm. Theoretical fitting results using the MKNVPB model exhibited excellent prediction alongside experimental data than conventional models. Subsequently, the MKNVPB constitutive equation was expanded into a three-dimensional differential form using C ++ and FISH language, followed by the secondary development integrating into FLAC 3D . Numerical simulations reproducing experimental loading conditions showed excellent agreement with the creep test curves. The results confirmed that the developed model accurately can simulate the full creep evolution of silty mudstone, especially in predicting accelerated creep behavior before critical failure.