Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.

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This work presents a novel model of sheared granular materials that consist of two-dimensional, slightly inelastic, circular disks. To capture the static and kinetic features of the granular flow involving different regimes, both the shear stress and pressure are superimposed by a rate-independent component ͑representing the static contribution͒ and a rate-dependent component ͑representing the kinetic contribution͒, as determined using granular kinetic theory. The dilatancy law is adopted to close the set of equations, and the constraint that static pressure is non-negative is utilized to determine the transition between the dense regime and the inertial regime. The balance equation of granular temperature incorporates the works done by both the static and kinetic components of shear stress. This enabled the proposed model to predict the hysteretic flow thresholds and the shear bands. Additionally, a thick, surface-driven granular flow under gravity is investigated using the proposed model. The predicted velocity, volume fraction, granular temperature, and stress are consistent with results obtained using the molecular dynamic method. This finding demonstrates the ability of the proposed model to simulate granular flow in which the quasistatic, dense, and kinetic regimes coexist simultaneously.