Abstract The morphodynamic evolution of the shape of dunes and piles of granular material is largely dictated by avalanching phenomena, acting when the local slope gets steeper than a critical repose angle. A class of degenerate parabolic models are proposed closing a mass balance equation with several viscoplastic constitutive laws to describe the motion of the sliding layer. Comparison among them is carried out by means of computational simulations putting in evidence the features that depend on the closure constitutive assumption and the robust aspects of the models. The versatility of the model is shown applying it to the movement of sand in presence of walls, open ends, columns, doors, and in complicated geometries.

中文翻译：

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滑坡的退化抛物线模型

摘要 沙丘和颗粒状物质堆的形态动力学演化很大程度上取决于雪崩现象，当局部坡度比临界休止角更陡时起作用。提出了一类简并抛物线模型来闭合质量平衡方程，该方程具有几个粘塑性本构定律来描述滑动层的运动。它们之间的比较通过计算模拟进行，证明依赖于闭包本构假设的特征和模型的鲁棒性。该模型的多功能性体现在将其应用于存在墙壁、开口端、柱子、门和复杂几何形状的沙子运动。