Modeling Time-Dependent Rock Behavior: Simultaneous Validation of Creep and Stress Relaxation Using a Combined Viscoplastic Approach

Abstract This study investigates the time-dependent mechanical behavior of rocks and granular materials, challenging the conventional view of their response as time-independent. We present a rheological model that effectively simulates active loading, creep, and stress relaxation in geomaterials, validated through laboratory experiments on a wet limestone sample. Traditional elastic and plastic models often fail to capture the complexities of rock behavior under prolonged stress, necessitating the use of viscoplastic models that integrate rate-dependent plasticity. Building on existing research, we developed a combined elasto-viscoplastic model featuring two groups of Shvedova–Bingham–Norton viscoplastic elements. The first pair accounts for elastoplastic deformation during active loading, while the second pair activates beyond a critical stress level, known as the D-point, at which significant microstructural changes occur. The model accurately captures the essential time-dependent behaviors of creep and stress relaxation, demonstrating excellent correlation with experimental data across all loading stages. Parametric studies reveal the model's unique behavior and its sensitivity to parameter variations, highlighting its robustness. This research contributes to the understanding of rock mechanics and provides a simplified yet physically interpretable framework for modeling complex deformation processes, facilitating practical applications in geotechnical, mining, and petroleum engineering contexts.