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

Abstract

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.