Abstract Numerical simulations of granular flows with Navier–Stokes type models emerged in the last decade, challenging the well established depth-averaged models. The structure of these equations allows for extension to general rheologies based on complex and realistic constitutive models. Substantial effort has been put into describing the effect of the shear rate, i.e. the magnitude of the velocity gradient, on the shear stress. Here we analyse the effect of the deformation type. We apply the theories of Mohr–Coulomb and Matsuoka–Nakai to calculate the stresses under different deformation types and compare results to the theory of Drucker–Prager, which is formulated independently of the deformation type. This model is particularly relevant because it is the basis for many granular rheologies, such as the μ ( I ) –rheology. All models have been implemented into the open-source toolkit OpenFOAM® for a practical application. We found that, within the context of these models, the deformation type has a large influence on the stress. However, for the geometries considered here, these differences are limited to specific zones which have little influence on the landslide kinematics. Finally we are able to give indicators on when the deformation type should be considered in modelling of landslides and when it can be neglected.

中文翻译：

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塑性屈服面的颗粒粘度：变形类型在颗粒流动中的作用

摘要 在过去十年中出现了使用 Navier-Stokes 类型模型对颗粒流进行数值模拟，挑战了完善的深度平均模型。这些方程的结构允许扩展到基于复杂和现实的本构模型的一般流变学。已投入大量努力来描述剪切速率的影响，即速度梯度的大小，对剪切应力的影响。这里我们分析变形类型的影响。我们应用 Mohr-Coulomb 和 Matsuoka-Nakai 的理论来计算不同变形类型下的应力，并将结果与​​ Drucker-Prager 的理论进行比较，该理论与变形类型无关。该模型特别重要，因为它是许多颗粒流变学的基础，例如 μ ( I ) – 流变学。所有模型都已在开源工具包 OpenFOAM® 中实现，以用于实际应用。我们发现，在这些模型的背景下，变形类型对应力有很大影响。然而，对于这里考虑的几何形状，这些差异仅限于对滑坡运动学影响很小的特定区域。最后，我们能够给出在滑坡建模中何时应考虑变形类型以及何时可以忽略变形类型的指标。