A Pressure-Sinkage Model for Deep-Sea Sediments Based on Variable-Order Fractional Derivatives

In order to better describe the pressure-sinkage process of deep-sea surface sediments, this article proposes a new four-element model. First, the pressure-sinkage process was divided into four components according to the change in the deep-sea sediment sinkage rate, and the time-dependent mechanical property of deep-sea sediments was described. Then, a new four-element pressure-sinkage model was established by introducing variable-order fractional derivatives into the modelling idea of classic element combination to describe the full pressure-sinkage regions of deep-sea sediments. Furthermore, by comparing with the experimental results from other literature, the proposed model was verified to predict the pressure-sinkage process of deep-sea sediments under static and dynamic loads. Finally, through a sensitivity analysis of model parameters, the effects of ground pressure and time on the law and mechanism of deep-sea sediment pressure sinkage were revealed. Results indicate that the deep-sea sediment pressure-sinkage process has obvious nonlinear characteristics and that the sinkage depth increases directly with ground-specific pressure and time. Through comparative analysis of both experimental and predicted results, the proposed pressure-sinkage constitutive model can describe the stress-strain of the full stages. Thus, the variable order model represents an effective method to predict the pressure-sinkage process of deep-sea sediments.