Modeling the creep behavior of hydrate-bearing sediments using a variable-order fractal derivative

Natural gas hydrate, which contains large amounts of methane, is a potentially vast and untapped source of clean energy. It forms under high-pressure, low-temperature conditions, typically found in deep-sea sediments. However, long-term exploitation of these resources poses several geoengineering risks, with creep deformation in hydrate-bearing sediments (HBSs) being a critical factor in predicting geohazards. In this study, a multistep loading test is employed to model the complex time-dependent deformation of HBSs. In this model, a variable-order fractal derivative is introduced to capture the nonlinear viscoelastic–plastic strain behavior of HBSs, featuring straightforward parameter identification, transparent physical meaning, and exceptional computational efficiency. The proposed model can predict the creep behavior of HBSs under various loading path. Comparisons between model predictions and experimental results show that the model successfully describes the entire failure process, particularly the accelerated creep phase. These findings are significant for predicting the nonlinear failure behavior of natural gas hydrate reservoirs during extended exploitation.