The driving performance of subsea mining vehicles is greatly affected by the pressure–sinkage characteristics of deep-sea sediment. Therefore, it is of great importance to analyze the microscopic properties of deep-sea sediment and establish the corresponding pressure–sinkage model for the safe operation of subsea mining vehicles. Hence, the present paper focuses on the physical properties of deep-sea sediment to provide a preliminary understanding of its pressure–sinkage process and evolution according to the solid–liquid two-phase flow characteristics and particle flow mechanism. In addition, the stress loading time and the rheological theory are applied in order to introduce a four-element model that describes the various pressure–sinkage stages that correspond to each stage of deep-sea sediment evolution. On this basis, the parameters of the pressure–sinkage constitutive model are determined by a specific calculation method. Moreover, a new pressure–sinkage constitutive model of deep-sea sediment that considers the time-variable mechanical properties is established in order to describe the full sinkage process. Finally, research results from the existing literature and experimental data are used to verify the rationality and correctness of the model. The results show that the proposed pressure–sinkage constitutive model is in good agreement with experimental data and is effective in describing the evolution of the mechanical properties and the trend in the sinkage rate of deep-sea sediment at various stages. A comparison with the Kelvin model indicates that the proposed pressure–sinkage constitutive model provides superior accuracy with the use of fewer parameters. Consequently, this study can provide a theoretical basis and technical support for the design of subsea mining vehicles.

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.

Estimating contaminant transport is of great importance for water quality assessment and water resources management. Due to the complex mechanisms and three-dimensional (3D) variability, estimating the concentration field of effluent mixing and transport is a challenging task. It is not practical to establish spatiotemporally high-resolution observation networks for monitoring contaminant mixing phenomena; thus, it is meaningful to develop mathematical approaches to predict the relevant processes. However, the applications of analytical or simplified numerical models are typically restricted to comparably simple cases. Sophisticated numerical models based on the 3D computational fluid dynamics (CFD) technique can provide accurate predictions, but they are computationally expensive and require high-level 3D CFD expertise, impeding their widespread usage.The recent developments in machine learning (ML) techniques and computing resources have provided a new avenue for investigating complex physical processes. Deep learning (DL), which is a subset of ML, has recently been applied to various water-related problems, and has been demonstrated to be a powerful tool for the community of water resources research. Thus, DL is potentially a promising candidate tool for modeling effluent mixing and transport.To assess the suitability of DL in modeling effluent mixing and transport, we focus on a classic example: the mixing and transport of multiple buoyant effluents discharged vertically into stagnant ambient water. This is a very important example for effluent mixing and transport. First, investigating this phenomenon itself is crucial for environmental assessment and water resources research, especially because wastewater effluents from

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