Slow and very slow landslides can cause severe economic damage to structures. Due to their velocity of propagation, it is possible to take action such as programmed maintenance or evacuation of affected zones. Modeling is an important tool that allows scientists, engineers, and geologists to better understand their causes and predict their propagation. There are many available models of different complexities which can be used for this purpose, ranging from very simple infinite landslide models which can be implemented in spreadsheets to fully coupled 3D models. This approach is expensive because of the time span in which the problems are studied (sometimes years), simpler methods such as depth‐integrated models could provide a good compromise between accuracy and cost. However, there, the time step limitation due to CFL condition (which states that the time step has to be slower than the ratio between the node spacing and the physical velocity of the waves results in time increments which are of the order of one‐10th of a second on many occasions. This paper extends a technique that has been used in the past to glacier evolution problems using finite differences or elements to SPH depth‐integrated models for landslide propagation. The approach is based on assuming that (i) the flow is shallow, (ii) the rheological behavior determining the velocity of propagation is viscoplastic, and (iii) accelerations can be neglected. In this case, the model changes from hyperbolic to parabolic, with a time increment much larger than that of classic hyperbolic formulations.

中文翻译：

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针对缓慢滑坡的深度集成 SPH 框架


缓慢和非常缓慢的山体滑坡可能会对建筑物造成严重的经济损失。由于它们的传播速度，可以采取计划维护或疏散受影响区域等行动。建模是一个重要的工具，可以让科学家、工程师和地质学家更好地了解其原因并预测其传播。有许多不同复杂性的可用模型可用于此目的，从可以在电子表格中实现的非常简单的无限滑坡模型到完全耦合的 3D 模型。这种方法很昂贵，因为研究问题的时间跨度（有时是几年），深度集成模型等更简单的方法可以在准确性和成本之间提供良好的折衷。然而，由于 CFL 条件（规定时间步长必须慢于节点间距与波的物理速度之间的比率）而导致时间步长限制，导致时间增量约为十分之一的量级。本文将过去用于解决冰川演化问题的技术扩展到滑坡传播的 SPH 深度积分模型。是浅的，(ii) 决定传播速度的流变行为是粘塑性的，并且 (iii) 可以忽略加速度。在这种情况下，模型从双曲线变为抛物线，时间增量远大于经典双曲线公式的时间增量。 。